"We're hoping the case will move quickly," said Aaron Sarver of the North Carolina-based gay-rights organization Campaign for Southern Equality.
As reported The Clarion-Ledger, in addition to its gay marriage ban, Mississippi prohibits same-sex couples from legally adopting a child or being listed together on a child's birth certificate. It also prevents them from sharing public employee retirement and health benefits, making medical decisions on their partners' behalf and being appointed administrator of the other's estate.
Rebecca Bickett and her partner Andrea Sanders, who wish to marry in Mississippi, Jocelyn Pritchett and her wife Carla Webb, married in Maine, decided to change that.
"My family is no less a family than any other," Bickett said in a statement.
"It's time we are able to live with legal protections in our home state," Pritchett added. "We love Mississippi. It is home for us and we have many beautiful friends and family members here."
The Governor of Mississippi, Phil Bryant, a Republican, has already warned that he would defend the law through.
If the court finds the ban unconstitutional, the appeal will join the case of Texas and Louisiana in the 5th Circuit Court of Appeals in New Orleans.