Regardless, Caren and Brian had a church wedding in Virginia, one of 25 states where cousin marriage is legal.
"We talked to our minister. … And he knew and he didn't have an issue with marrying us," said Brian.
One of the reasons cousin marriage is taboo, is the assumption they will have kids with birth defects.
But a new groundbreaking study funded by the National Society of Genetic Counselors revealed that some beliefs about cousin marriage were unfounded.
Robin Bennett, who headed the study, told ABC News that the risks of having a child with a cousin were about "2 [percent] to 3 percent" above the average population's risk for having a child with birth defects or mental retardation.
She says while there are risks, they're "not as bad" as people perceive.
Other risk factors are higher. For example, there's a 10 percent chance that a 41-year-old woman will give birth to kids with chromosomal defects.
If one parent has a genetic disease, like Huntington's, they have a 50 percent chance of passing it on.
Bennett gives parents the risks but will not tell them not to have kids.
She advocates that cousins who are romantically involved have genetic counseling before they get pregnant.
Brian and Caren went for counseling and were told the risk for birth defects was low, but their kids might have asthma, which runs in the family.
They now have two boys, ages 14 and 10, and both have asthma. But they don't think twice about their parents being cousins. They're also at the top of their classes in school.
The rest of the family has come around and say they couldn't be happier with how things have worked out.
Ultimately, Caren and Brian say it may have been their family connection that led them to fall in love.
"We could communicate," Brian said. "We had the same values, as far as raising children. … It's a match."
This story was originally broadcast on "20/20" Aug. 6, 2004.