So, if I get this straight.
It's a joint mortgage of which he doesn't want the monthly payments anymore and want to clear his half (yes, we all know legally he is responsible) but his "moral" half (as the current situation lies).
So he pays 50k off of the remaining 100k, is he then expecting your monthly payments to half, just leaving you half to pay ?
I mean, if you both keep your finances separate, and your mortgage would in fact work like that, I don't see a problem for you. if you remain only paying your fair half and it can remain as so until paid off.
I'm assuming the remortgage will be in joint names for the ease of the remortgage and to keep his name on it etc., but still just remain for you to pay, any difference in rate though may need adjusting so he contributes, but I'm not sure how I would work that out if I'm honest.
You have already said he steps up and covers everything when/if needed, surely this is more of a risk to him than you as if it were to go Pete Tong, he is still liable for half of the remaining mortgage ?