A spokesman for Ohio Attorney General Mike DeWine, whose office will fight the lawsuit, declined to comment.
Previously, DeWine has said he has a duty to defend Ohio's constitution and statutes, including the statewide ban on gay marriage, passed overwhelmingly by voters in 2004. Gay marriage supporters are working to put the issue back on the Ohio ballot in November.
The other plaintiffs in Monday's lawsuit are three lesbian couples living in the Cincinnati area who married in states that have legalized gay marriage. One woman in each of those marriages is pregnant through artificial insemination, and their babies all are due to be born this summer in Cincinnati hospitals.
The couples say they're worried that having only one of them listed as a parent on their children's birth certificates could lead to problems down the road, such as a denial of parental rights to the one not named should their partner die or experience a medical emergency.
"I have no legal grounds to stand on. That's not something that should be happening in our society," said Pam Yorksmith, who married her wife in California in 2008. The couple has a 3-year-old son and another on the way.
The couples' attorney is the same one who represented two gay married couples in their lawsuit last year that successfully sought a court order forcing Ohio to recognize same-sex marriages on death certificates. The state is appealing the ruling, issued in December by federal Judge Timothy Black.
"At both ends of our lifespans, a marriage is a marriage. A family is a family," said the couples' lawyer, Cincinnati civil rights attorney Al Gerhardstein. "A family is a loving, nurturing group of people and the identification document when the children come along is the birth certificate, and it ought to be right."
Unlike Oklahoma and Utah, where federal judges recently struck down gay marriage bans, Gerhardstein is working to slowly chip away at Ohio's gay marriage ban through narrow lawsuits.
He referred to the Cincinnati-based 6th U.S. Circuit Court of Appeals, saying he didn't think its judges would uphold a ruling similar to the Oklahoma and Utah cases but would be more open to the argument he's making that a state cannot disavow a marriage that was legal in the state where it took place.
Gerhardstein's tactic also will give the U.S. Supreme Court a wider variety of legal arguments to consider when appeals from various states reach their chambers.
Gerhardstein hopes his successful gay marriage lawsuit last year acts as a stepping stone to a victory in Monday's lawsuit.
In last year's case, Judge Black ruled that Ohio's ban on gay marriage demeans "the dignity of same-sex couples in the eyes of the state and the wider community."
"Once you get married lawfully in one state, another state cannot summarily take your marriage away," Black wrote, saying the right to remain married is recognized as a fundamental liberty in the U.S. Constitution.
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