Generally, the spouse who incurred debt during the marriage is solely responsible for paying it back. For example, if one spouse took out a car loan in his name, the other spouse will generally not be liable for repayment of same.
Generally, both spouses are equally responsible for paying the full amount of joint debt. For example, if both spouses opened a joint line of credit, they will both be responsible for the full amount owed. Creditors can then pursue both spouses for the repayment of same. Accordingly, if one spouse does not pay his share of the joint debt, the other spouse may be liable for the entire amount.
Often, separation agreements stipulate which spouse will pay which debt(s). However, these agreements are not binding on third party creditors. Thus, one spouse might still be liable for the other spouse’s debt, notwithstanding a clause in the separation agreement to the contrary.