In some cases he can. It depends on whether the payment of the debt is characterized as support. Many divorce decrees specifically include payments of marital debts as support obligations to make it easier for the receiving spouse to prevent the paying spouse from discharging the debt. Even if yours does not, the bankruptcy judge can review the judgment to determine whether that is what was intended.
The intent of the decree controls how the debt will be treated in bankruptcy. If the final decree lists the debt in a section entitled, “Division of Debts”, it will most likely be considered a consumer debt instead of a support obligation. If it is a consumer debt, then your ex-spouse can avoid paying the debt by declaring bankruptcy. An unfortunate consequence is that the creditor may then come after you. Many spouses are frustrated by collection activities such as these because they thought the divorce petition protected their financial future. Because creditors were not parties to your divorce, they are not bound by the decree of divorce and may still come after you for the debt. Your remedy will be a separate cause of action against your ex-spouse by way of a motion to enforce the original divorce decree in the family court.