We have live with her for a year and a half..
Divorce / Separation Lawyer
You are probably talking about a "morality clause" that we stick in divorce decrees. The intent of those clauses is to prevent the children from being exposed to one parent's romantic interests, becoming attached to them, then suffering when the relationship blows up. They are not meant to get in the way of committed relationships--but they do.
Your morality clause can be written two ways. The most common wording says something like this: "Neither parent shall permit a person of the opposite sex to remain in the house while the children are in that parent's care." If that's what your decree says, then a same-sex relationship would not technically fall under that prohibition.
Some family law attorneys word is more like this: "Neither parent shall permit a person with whom they are involved in a romantic or dating relationship to remain in the house overnight while that parent has possession of the children." If it's worded more broadly like that, then yes, it would prohibit your same-sex relationship if it's more than just being roommates.
If your decree does not contain EITHER of these provisions, then your husband may be out of luck in terms of enforcing a "morality clause." HOWEVER: Given Texas's hostility to same-sex relationships as well as spotty tolerance of them, you need to consult with a local family law attorney who can tell you if the judge in your case would enforce it against you.
If there is no morality clause to enforce, there are other arguments your husband could make. But here's the deal. He can't make you break up your relationship. What he can do is ask the court to modify the parent child relationship so that you don't have overnight visits if you violate the court's order. That's a serious consequence--for both you and him.