I see. Thank you for the additional information, Beth.
It is not typically automatic that a spouse who is awarded property during the marriage must refinance that property unless the decree specifically requires them to do so. And the deed of trust or quit claim deed signed by you would normally transfer ownership of the property to your ex, but have no effect with regard to the mortgage.
It sounds as though someone may have mistakenly omitted the language in the decree requiring him to refinance within a certain period of time or the property would be sold. Since that language is not included in the decree, you may wish to negotiate with your ex with regard to this issue, perhaps offering to forgive some portion of the payments he owes you in return for his refinancing the mortgage.
I would NOT agree to sign title of the property over to him until he has refinanced either, since then you would continue to be liable on an asset which you do not own. Perhaps if he is anxious to have you sign over title to the property, he will agree to refinance the mortgage in return for that.
So your leverage to compel him is that he wants your name off the title and the fact that he must pay you a monthly amount. Those two things can be used to motivate him to refinance.
However, if he pays off the mortgage, as you suggest may occur, in that case, refinancing would not be necessary since the debt you are obligated to repay would have been satisfied.
I hope this helps clarify the situation for you. Please remember to rate my service once you have all the information you need. If you have any other questions, please ask me – I’ll be happy to respond. Thank you!