The father, an engineer, saw no future for his daughter and son in their struggling country, Ecuador. In 2001, he made his way to Mexico and paid smugglers known as "coyotes" to help him sneak across the border into Texas. Then he headed to New York, where his wife and children flew in as tourists and stayed.

But the consequences of that decision—an immigrant's uprooting his family for the sake of the next generation—have been anything but simple.

His daughter, now 22, graduated from college with honors, and is still living in the U.S. illegally. While her classmates have good corporate jobs and take foreign vacations, she's a bookkeeper for a small immigrant-run business. She fears venturing outside New York City and can't even get a driver's license.

Meanwhile, her 17-year-old brother—who was born in the U.S. and is therefore an American citizen—can do things his family cannot, like spending summers in Ecuador with his cousins. But he's lonely during the school year here and would like to move back to Ecuador.

"How can he even think that?" asks his mother. "We're sacrificing ourselves so he can get a better education and a better job. After giving up everything to come here, he—the only one with papers—wants to go back?"

Citizen & Non-Citizen Children

This family of four—who let a reporter and a photographer spend time with them only if they were not identified, for fear of being deported—is part of a growing group of what are often called mixed-status families.

Nearly 2.3 million undocumented families—about three quarters of those that are in the U.S. illegally—have at least one child who is a U.S. citizen, according to the Pew Hispanic Center in Washington, D.C.; nearly 400,000 families have both citizen and non-citizen children.

The increase in mixed-status families is due to a tide of illegal immigration and federal laws that deny legal status to illegal immigrants' foreign-born children—who had no say in coming here—while granting citizenship to their American-born siblings.

And as their numbers rise, they are challenging three of the biggest stereotypes of immigrants today.

The first stereotype is that immigrant families are either legal or illegal. The second stereotype is that they either know they're here to stay or bent on returning home. The third is that most immigrants are men on their own, without wives and children.

In fact, most immigrants live in families, and with a blend of legal statuses, opportunities, and plans. This family, in Queens, New York, shows how such disparities within immigrant homes can pull family members in such different directions.

Mother, father, son, and daughter are now split between two households, and between those who expect to stay in the U.S. and those who want to return to Ecuador. The daughter, despite tireless efforts to get ahead, feels she is losing ground and that her brother—who carries the weight of his family's highest hopes—takes his citizenship for granted.

The mother, 47, who gave up her job in Ecuador as a computer systems analyst and now babysits for a living, has tried in vain to leverage her son's citizenship to get a green card, which would grant her permanent legal residency.

Still, they are better off than many illegal immigrants. They have built a comfortable life in New York, a city that has traditionally welcomed foreigners, regardless of whether they have immigration papers. And the parents are among a rising proportion of illegal immigrants with higher educations—about 25 percent have had some college—abandoning careers back home to come to the U.S. to vault their children into the American middle class.

The daughter showed promise at age 7, when she was already working the cash register at her parents' office-supply shop in Ecuador, and by the time she was 9, she was absorbed in math. As she neared her 14th birthday, her father began to think about taking his family back to the United States so she could go to college here.

The family had been here before. After graduating at the top of his class from the polytechnic university in Quito, Ecuador's capital, the father moved to New York in 1986—legally, on a student visa—to study for a graduate degree in engineering. He planned to return home to his wife.

But when he learned that she was expecting their first child, he quit school and took a factory job—which violated the terms of his visa—and arranged to have his wife and baby daughter smuggled into Texas and travel to New York.

"I knew I was passing into illegality," he says. "It was a very difficult decision to make. But I had to support them."

They all eventually moved to Miami, where their son was born. But hopes of a prosperous American life eluded them, and in 1992 they returned to Ecuador.

As their daughter raced through school, skipping two grades and outpacing her classmates, her father worried about the quality of schooling in Ecuador, where the economy was slipping into chaos. He resolved to give her, and her brother, the American education he never completed.

No Social Security Number

When they arrived in New York in 2001, the father found work as a draftsman with a construction company. He earns more than he would in Ecuador, and enjoys the chance to showcase his skills and move around the city, working in nice office and apartment buildings. The mother, on the other hand, cares for other people's children in cramped apartments.

These discrepancies put a strain on their relationship, and four years ago they separated. The children spend most weekdays with their father, in the attic of a house in Queens owned by his brother, who is a legal resident. On weekends, they visit their mother in her basement apartment in another neighborhood.

The daughter is among 65,000 young people who graduate from American high schools each year without immigration papers, according to the Urban Institute in Washington, D.C. She began to understand just what that meant when she talked to a guidance counselor about college.

"She asked me for my Social Security number," the daughter recalls. "She said she couldn't help me with applications without one."

She quickly learned the other things she couldn't have, like scholarships and the chance to attend college outside New York. And it is nearly impossible for illegal-immigrant children to become legal residents without going back to their native country, and then waiting 10 years to apply.

For the daughter, going back to Ecuador is out of the question. "All my friends are here," she says. "All I know is here. If I returned, I'd be lost."

Luckily, she lives in New York, one of 10 states that allow illegal immigrants to pay resident tuition rates at public universities. With $5,000 a year from her father and a babysitting job, she attended a highly ranked college in the City University of New York, earning a 3.8 GPA in accounting.

Overqualified & Underpaid

But she still lacked the Social Security number needed to apply for jobs and internships. While friends—many of them children of legal immigrants—landed $70,000-a-year jobs, she sought out small businesses willing to risk hiring her for half that.

"Sometimes I felt like crying or screaming," she says. "Some of my friends knew why I didn't apply for corporate jobs. But other people who didn't know would criticize and judge me. They thought I was lazy or stupid."

She was eventually hired as a bookkeeper by a small company that, ironically, provides immigrants with information on visas and citizenship. She is paid on the books—and pays taxes—thanks to the tax-identification number the federal government gives people without Social Security numbers.

Though overqualified and underpaid, she rarely complains. Instead, she and her boyfriend—a Mexican college student who is also here illegally—volunteer with an immigrant group pushing Congress to pass the Dream Act, which would grant legal status to high school graduates who were brought to the U.S. by their parents.

Her mother has a quicker solution: Dump the boyfriend and marry an American. At first, the daughter was shocked at the idea of marrying for reasons other than love. But she's begun to waver. "I'm thinking it might be worth a try because this is so frustrating," she says.

Her brother, on the other hand, is tightly tied to Ecuador. As the only family member who can travel freely, he's spent three summers there with his cousins. Back in New York, he's in touch with them by e-mail and on Facebook.

He seems much less connected to New York, where he comes home after school to an empty apartment to do homework. But his family insists he stay in the U.S.

His father doesn't want him to go for the quick money that leads other boys in the neighborhood to drop out of school to work at delis or construction sites for $500 a week. He closely follows his son's schoolwork, and meets often with his teachers.

The daughter thinks that her brother "doesn't see how difficult it is for us not having documents. And he sees how it is for me—I can't go back to Ecuador or get a better job."

For now, her brother has stopped talking about going back to Ecuador and started thinking about going to college in the U.S. to study architecture. But he still feels the pressure that many citizen-children of illegal immigrants experience.

"Maybe they expect too much of me," he says. "But my family wanted me to come here. It's better for me, and better for my sister."