Legal Question in Family Law in Texas

Texas does not have common law marriage. Texas does recognize informal marriage in some limited circumstances where the man and woman are not married to anyone else, agree to live together as husband and wife, do live together as husband and wife, and hold themselves out to the community as husband and wife.

If you are asking whether you can sue your husband's mistress, the answer is probably not. It depends on what you want to sue for. If you want to sue her because he engaged in conjugal relations with her, you can't do that.