You are responsible for all marital debts incurred by either spouse between the date of the marriage and the date you file for divorce. Debts from before marriage or after the date you file for divorce are separate property (and responsibility) of whoever incurred them.
Even if you are separated from your spouse, you may be responsible after separation for accounts that are in both of your names or in the name of either spouse with businesses that are accustomed to dealing with you as a couple and have not been notified that you are separated and want your name removed from the account.
It is a good idea to give these creditors notice in writing of your separation/filing for divorce.
You will always be liable for any debt for which you were originally liable when it was incurred. If your spouse is ordered by the court to pay a specific debt and your spouse fails to pay it, the creditor can demand payment from you, or repossess any marital property that secured the debt.