The American Civil Liberties Union is suing to overturn North Carolina's treatment of same sex parents. The practice that prohibits non-married couples from being able to adopt children first surfaced in 2010. The affect of the law, the lawsuit claims, is to unconstitutionally prevent caring parents from adopting the children they are raising with their partner.

The opinion that spurred the initial shift in policy dealt with a situation in which a biological parent had not terminated their parental rights with the child. The typical representation of this requirement is when you have a birth mother and/or father who terminate their rights at the birth of the child so that the adoptive parents can adopt him or her. The problem, then, is when one of the parents in a same-sex couple is the biological parent, and the other is not, eventhough the parents have agreed to raise the children collectively as their own.

“Children who are prevented from having such a legally recognized relationship with both parents suffer numerous deprivations as a result, including exclusion from private health insurance benefits, public health benefits, veterans’ benefits, disability benefits and social security benefits,” the lawsuit says.

While adoption laws generally vary from state to state, the courts in 10 states, which include California, New York, and Pennsylvania, and the District of Columbia, have held that their adoption statutes permit second parent adoptions (i.e. non-married parents) because they’re in the best interest of the children.
As one woman said of her situation, “We planned to have our children together…She attended every prenatal appointment. She was with me at the birth of our children. She has changed countless diapers. She spent hours rocking each of our children and sharing in the responsibilities and joys of motherhood.” And yet, if the non-biological parent should somehow be out of commission, the other "parent" would potentially have no legal recourse.
It will be interesting to see how the resolution of this case, and those like it (e.g. in FL)  ties in with the current legal trend attacking DOMA and its unequal treatment of benefits and the like.