She's Off the Deed

Who are the "they" who said he'd have to refinance?  If it was the mortgage lender, that's that.  But otherwise, it's worth contacting the lender to see if they'll relieve you of liability.  Sometimes they'll agree to do that, assuming your husband can prove he's financially qualified to carry the payments on his own.

If that can't be done, you may want to hesitate about signing off on the house.  I sometimes hear from people who did that, and whose ex-spouses later won't or can't refinance. Lenders don't have to obey that divorce decree, and sometimes people get stuck with the debt or with credit problems, even though they no longer own the house.