While same-sex couples gained the right to marry and have that marriage recognized in all 50 states, other family-oriented laws have not yet caught with this new reality. Same-sex couples may assume that, upon divorce, they are entitled to a joint custody arrangement, the same as heterosexual couples. But they would be wrong. Unfortunately, many state laws still rely on the notion of "biological parentage" which can impede a same-sex partner from contesting their parental rights. This post will go over biological parentage and how it may affect you.
Most states still assign parentage based upon the biological relationship to the child. That means a DNA donor to a same-sex couple is the legal guardian of the child. Furthermore, the non-biological parent has no legal parental rights to the child.
The only way to rectify this issue is through an adoption by the nonbiological parent. But adoptions are only valid if the other biological parent surrenders his or her parental rights. That means same-sex couples must obtain the consent of the biological parent (not always a guarantee) before the nonbiological parent can formally adopt the child. Once the adoption goes through, the nonbiological parent gains parental rights and can fight for custody in the event of a divorce.
As you can see, obtaining a joint custody arrangement is not automatic. You must qualify as a legal parent. A lawyer can help you go through the adoption process to help ensure that your parental rights are protected in the event of a divorce. Don't risk your right to raise your child. Until the laws are changed, this is the process to secure your parental rights.