This question cannot be answered without more info. If the debt was personal to your spouse, as opposed to purchases that benefited the household or any children, then oftentimes the person incurring such debt would be responsible for it.
This type of issue is something that is normally negotiated as part of the property division during divorce. The other component with this issue is that if bills are not paid, and the debt was joint, then creditors can look to both parties for payment.
Hope things go smoothly for you.
Stephen McDonough, Esq.
It is not automatic, and if the two of you cannot agree, the judge will review the facts leading to the debts, and make a decision after a trial.