Legal Question in Family Law in Texas

the exact answer to this question will depend on which you were divorce decree says.

The wording in the decree is important.

Probably, what should happen is this: your husband will sign a quitclaim or a special warranty deed that will transfer all of his interest (in the house) to you. You can take this document and record it at the County Clerk's office among the deed records.

The debt owed on the house is a different matter entirely. It isn't possible just to switch a debt from one name to another; that would require the cooperation of the bank, and the bank is not a party to your divorce.