I have a friend who is in the process of going through a divorce. She wants to buy her own place, but to qualify for a loan she has to get her name off of the mortgage she has with her H. As far as I know, her H who is going to retain the mortgage is not having to refinance, he just has to file paperwork assuming full responsibility. However it may be that he has be able to qualify with his income alone in order to get permission to have her removed. If that makes sense.
In order to count what your H is providing you, I'm pretty sure the bank would want to see something legal in writing that he is obligated to pay you.