Question about debt and getting a mortgage?

My husband & i have a lot of credit card debt (mostly in my name) and he is a authorized user on 2 of my cards. We are looking to buy our home, my mom currently owns the home and will be giving us a gift of equity around 20,000 maybe more. 10 years ago it was valued at 110,000 and now i'm not sure what it is but i'm uming at least 20000 in equity. Would it be better for my husband to get the mortgage alone or with me? I have no income and carry majority of the credit card debt. We also have 2 car payments. i am a co-signer on his and he is a co-signer on mine. If we do the mortgage with it only in his name can the bank use my car (that he is a co-signer on) and my credit cards (that he is a authorized user on) against him when figuring his debt to income ratio?