MONTPELIER, Vt. — Frances Herbert and her wife, Takako Ueda, were looking forward to the New Year’s Eve family concert at the Baptist Church, the town fireworks on the pond and then a night at home to celebrate the arrival of 2012.

But federal immigration authorities have told Ueda she needs to leave the United States for her native Japan by Dec. 31, a move that would split up a couple who have been together more than a decade and were married under Vermont law in April.

Their relatively rare case illuminates the difficulties that binational gay couples face at a time when the Obama administration has pledged not to uphold federal marriage law in courts but the rest of the executive branch — including immigration authorities — still follows the letter of the law.

Federal immigration authorities demand extensive documentation showing that a binational couple claiming to be married really are: witness statements, property records, utility and other household bills showing both names and the like often are required. Herbert said she and Ueda submitted 600 pages of such evidence with their application.

“It’s despicable,” Herbert said. “We had 600 pages of proof, and 599 of them were completely ignored. one line on one page” — the one that said they were both women — “is what they paid attention to.”

Herbert, a 51-year-old home care provider, and Ueda, a 56-year-old graphic designer, live in the southern Vermont town of Dummerston and got letters Dec. 1 from U.S. Citizenship and Immigration Services, a division of the Department of Homeland Security, telling them that Ueda had to leave the country within 30 days. Ueda’s student visa expired in July.

They had applied for “relative alien” status on the basis that she was the spouse of a U.S. citizen, but the federal agency denied that petition.

The letter to Herbert, who had applied to be Ueda’s sponsor, said that under the federal Defense of Marriage Act, the 1996 law saying the government would not recognize same-sex marriages, they couldn’t be considered spouses. DOMA defines marriage as “only a legal union between one man and one woman as husband and wife.”

“Your spouse is not a person of the opposite sex,” wrote Robert Cowan, a U.S. CIS official. “Therefore, under the DOMA, your petition must be denied.”

Only a handful of states recognize same-sex marriages. Experts say there are not reliable numbers on how many couples find themselves in a similar situation to that of Herbert and Ueda, but it’s believed the number is small. Many binational same-sex couples don’t seek spousal status for fear of being rejected because of DOMA.

Steve Ralls, spokesman for Immigration Equality, a nonprofit legal aid group that works on immigration and sexual orientation issues, said one San Francisco couple remained together despite getting government notices that one of the men, an Australian, needed to leave the country, while a New Jersey man’s partner had been deported to Peru.

President Barack Obama and Attorney General Eric Holder Jr. announced in February that the administration would no longer defend DOMA in court in the cases in which it is being challenged. but until the issue is resolved, executive branch agencies, including those within the Department of Homeland Security, it remains the law of the land.

But Leslie Holmans, second vice president of the American Immigration Lawyers’ Association, said that even after getting the types of letters Herbert and Ueda got, some same-sex, binational couples benefit from “prosecutorial discretion” by immigration authorities.

She said many federal prosecutors believe “our systems are so overcrowded that what we really need to be doing is concentrating on people who are a risk to our country. What’s happened is that we have seen some same-sex couples go before the immigration court and ask for prosecutorial discretion.” Government lawyers often respond by “either dismissing cases or they’re not enforcing the notice of deportation.”

Holmans said the situation is far from ideal because affected immigrants are left in “legal limbo,” still without recognized immigration status and unable to get a job or seek other government benefits.

Scott Titshaw, a professor at Mercer University Law School in Georgia who has practiced immigration law and written articles on DOMA, said Ueda and Herbert most likely shouldn’t fear Ueda’s imminent arrest but “still have plenty to worry about.” He said if Ueda traveled abroad, then she might be barred from re-entering the U.S. With local authorities in some states cracking down on illegal immigrants, Ueda might also want avoid travel to places like Arizona and Alabama, which both have strict immigration laws.

Deportation could split up lesbian Vermont couple