Hello
I am in the same position but that of your h's ex.
Jointly owned a house with mortgage and then split.
Couldn't afford to buy him out and he couldn't afford to buy me out. This was due to it being a financially abusive relationship and so my credit was shot to bits, so I didn't have the option to remortgage as would have been refused a mortgage, even though I can easily afford the payments now he's not taking all my money.
We came to an agreement that I would give him a lump sum (my family provided this) if he agreed to remove his name from the deeds giving up his legal right to the house.
This was done via a solicitor. For it to be changed with land registry, it had to be agreed by the lender (mortgage company). Part of their conditions was that it had to be done through a solicitor so we both understood the implications. They agreed he could remove his name from the deeds but would remain on the mortgage. I'm guessing as it gives them two of us to chase if they ever needed to should payments not be made. It means that regardless of him being on the mortgage he has no legal claim to the property and it is now in my sole name on the deeds.
He will remain on the mortgage until it is paid and ends unless I remortgage before then.
I intend to remortgage as soon as I can and have been furiously working on improving my credit history. However I couldn't be forced to do this and am only looking to do so as I would like to see if I can get a better rate. I also understand his circumstances might change and although right now he has no intention of taking out a mortgage he might want to in future and this would hinder him. I just feel it's the right thing to do. He was a shitty person to me but that doesn't mean I'm going to be one in response.
Due to the nature of the agreement and that in future if he wanted to take a mortgage out his affordability would be affected due to him being on another mortgage (albeit with no legal claim to that property) he was advised to take independent legal advice before he agreed to coming off the deeds. He did and decided to go ahead anyway.
It sounds like your h didn't understand the implications of what he signed at the time. Did he take legal advice before signing the deed of transfer?