Name is on deed...Proof that he isn't responsible?!? Help!?

My mother and father are divorced but my fathers name is still on our deed. My mother is remortgaging the house and applied for the loan with ONLY her name on the application. Because his name is still on the deed he was required to sign several papers. He is concerned about that and basically freaking out. He wants to know for sure that since he isn't on the loan application that it won't affect his credit or leave him responsible. The mortgage bills do NOT have his name on them. Please help. Is this true? Is there any way to give him proof?