A gay couple married in New York said Friday that they have dropped their federal lawsuit seeking to force Ohio to recognize their marriage.

Al Cowger Jr. and Tony Wesley Jr. have been together for 28 years and married in upstate New York in June 2012. The couple lives in Gates Mills, a suburb of Cleveland, with their 8-year-old adopted daughter.

The couple said in their lawsuit filed last month that because Ohio would not recognize their out-of-state marriage, they were unable to enroll as a family under the Affordable Care Act (ACA) and were forced to purchase three individual policies at a higher cost.

Al Gerhardstein, the couple's attorney, said that the couple obtained a family policy on Monday that takes effect next month.

ā€œI can't tell you exactly where the hang up was,ā€ Gerhardstein told the AP. ā€œI think maybe it just needed that spotlight that came from this case and from the inquiries, and then the wheels got greased.ā€

Two weeks ago, the Obama administration said that starting next year insurers must offer identical health coverage to spouses in a same-sex marriage as they offer to spouses in an opposite-sex marriage.

Two lawsuits aimed at dismantling Ohio's ban, approved by voters in 2004, remain. However, those lawsuits seek to carve out exceptions to the ban, rather than topple it.

(Related: Four gay couples want Ohio to recognize their marriages on birth certificates.)