Unortunately, you will both be held liable for the debt. Even if a judge rules that one party is responsible for the mortgage, etc. If it is not refinanced, the debt belongs to both of you.
If your lenders agree to a short sale, you credit will not be impacted as greatly and you both should be free of the debt. Sometimes the lienholders will require a repayment plan of a portion of their losses before they agree to the short sale.