NEWARK (AP) – Almost two months after a law went into effect allowing same-sex couples to enter into civil unions, some couples say they are being denied health care coverage.

Civil unions offer same-sex couples the legal benefits of marriage – but not the title. New Jersey lawmakers last December passed legislation allowing civil unions in response to a state Supreme Court ruling two months earlier that said it was unconstitutional to deny same-sex couples access to the protections of marriage.

But Jennifer Bonfilio, who is planning to enter into a civil union with Shannan Hauser, said New Jersey Carpenters Funds, where Hauser is a union carpenter, said it wouldn’t allow her to be added onto the medical plan.

“I called to ask if they were going to be organizations honoring that law and providing me with the same coverage that they would any married couple, and I was told no,” Bonfilio, who pays more than $400 a month for health insurance, told The Star-Ledger of Newark for Sunday’s newspapers. “The woman on the phone actually said to me, ‘We do not have to obey New Jersey law.’”

Attorney David Buckel, who works for Lambda Legal, said he’s received many complaints from people being denied health care benefits. Some employers aren’t familiar with the law, he said, but others, such as self-insured employers or unions, can follow a federal law that allows coverage to be denied for same-sex couples.

George Laufenberg, administrative manager of the New Jersey Carpenters Funds, said his group is subject to federal law.

“Our understanding is we would not have to change our eligibility at this time to cover civil unions, but that’s not to say the trustees wouldn’t consider it,” he said.

According to Laufenberg, no written requests for health coverage for civil union couples have been received. Bonfilio said she is considering making that request.

Buckel said the state government is to blame for the problems because the Legislature decided to use the term “civil union” to describe the relationships.

“They have said that these relationships aren’t worthy of marriage,” Buckel said.

Steven Goldstein of Garden State Equality, which lobbies for the rights of same-sex couples, said his group has received 26 similar complaints.