Washington (CNN) A married same-sex couple living in London is suing the State Department over the determination that only one of their two sons is recognized as a US citizen.

According to a complaint filed in US District Court, US citizen Allison Blixt and her Italian national spouse, Stefania Zaccari, have two sons -- one carried by Zaccari and the other by Blixt. The couple say both children were conceived and born during their marriage, and they are both legal parents to their two sons, who, they argue should be eligible for US citizenship as a result.

However, the couple alleges the State Department notified them that Lucas, biologically born to Zaccari, is not a US citizen and was born "out of wedlock." The younger child, Massi, biologically born to Blixt, is apparently eligible for US citizenship.

"Allison and Massi may reside in the U.S. permanently because they are U.S. citizens," lawyers for the couple write in the court filing. "Stefania may reside in the U.S. permanently by obtaining a family-based immigrant visa based on her marriage to Allison."

"The State Department's policy, however, renders Lucas the only member of his family without the freedom to live in the U.S. permanently," the filing continued. "The State Department's decision to withhold from Lucas the same rights granted to his brother means that he will experience the indignity and stigma of unequal treatment imposed and endorsed by the U.S. government."

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