(CNN) -- Marcie Fisher-Borne carries a power of attorney with her at all times. She has a will but has made videos of her wishes for her children just in case someone contests them.

What if she were to get in a car accident tomorrow? What would happen to her daughter, 4, and her 6-month-old son?

It's not that Fisher-Borne doesn't have a partner -- she has been with Chantelle Fisher-Borne for 15 years. It's just that the state of North Carolina does not recognize same-sex marriage. Nor does it allow second-parent adoptions.

That means if Fisher-Borne were no longer capable of taking care of her children -- she gave birth to her daughter, and her partner, Chantelle, carried their son -- Chantelle Fisher-Borne would not be able to adopt their daughter.

The Fisher-Bornes were one of six couples listed in a federal lawsuit filed Wednesday by the American Civil Liberties Union that seeks to give full parental rights to same-sex couples.

"North Carolina's law denies children the permanency and security of a loving home simply because their parents are lesbian or gay," said Jennifer Rudinger, executive director of the ACLU of North Carolina.

"This is fundamentally wrong," she said. "No parent should have to worry about what will happen to their children if something happens to their partner."

A second-parent adoption is the adoption of a child by a parent in the home who is not married to the legal parent of the child, according to the Department of Health and Human Services. The first parent does not lose his or her rights.

In December 2010, the North Carolina Supreme Court banned such adoptions in the state.

In the lawsuit, the ACLU said a second-parent adoption is the only way that a family in North Carolina with gay or lesbian parents can ensure that both parents have a legal relationship with their child.

"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, social security benefits, life insurance benefits, and workers' compensation, as well as uncertainty about their ability to continue their relationship with their second parent if something should happen to their legal parent," the lawsuit said.

In some cases, a child could be taken out the only home he or she has known if the legal parent dies, said Chris Brooks, legal director of the ACLU in North Carolina.

Marcie Fisher-Borne recalled when she gave birth to her daughter. She was not even three hours old when a nurse at the hospital began questioning Chantelle's parental rights.

"We were treated as if our family was less than other families during what should have been one of the happiest occasions of our lives," Marcie Fisher-Borne said. "We don't ever want there to be any question as to who should care for our children. If something were to happen to either one of us, it could tear our family apart."

The lawsuit filed Wednesday argues that it is unfair that the state considers adoption petitions made by heterosexual stepparents on the merits of each case but will not do the same for same-sex couples because they cannot be legally married.

"Second-parent adoptions should be made on a case-by-case basis," Brooks said.

Same-sex marriage has long been outlawed in North Carolina, and in May, voters approved a referendum that made the ban a constitutional amendment.

Leigh Smith and Crystal Hendrix are also named as plaintiffs in the lawsuit.

The couple has been together for more than seven years. They have a 7-month-old child.

Hendrix gave birth; Smith stays at home to care for their child. The two women said they fear the consequences of Smith not being recognized as a legal parent.

"Ms. Hendrix's parents do not accept Ms. Smith, and do not recognize her as (their child's) second parent," the lawsuit said. "As a result, both Ms. Smith and Ms. Hendrix are concerned that if Ms. Hendrix were to die or become incapacitated, her parents would attempt to interfere with Ms. Smith's custody (of the child)."

They are hoping their lawsuit will help change the situation.