The short answer is both spouses are responsible for debts during a separation. They are still married and therefore usually still jointly on the hook for debts they incurred during their union.
Marriage is a legal status
Marriage is, among other things, a legal joining of two people. Earning by one spouse is generally considered jointly owned, and debts are jointly held as well. At divorce, the court will ensure the spouses have fairly split their assets and liabilities. Most often, the parties will agree on a split and the court will simply approve it. Other times, lawyers for each spouse will argue over the split and the court will have to make a ruling.
Separation means living apart but legally bound
When a married couple is headed towards a divorce, a separation is usually the first step. It may seem like common sense that a married couple that wants to divorce will separate themselves physically. Most commonly, this means that one spouse will move out of their shared home. This separation, sometimes called “living separate and apart,” has an important legal consequence as well. Many states require a separation period before a divorce, often a whole year.
A lot can happen during the sometimes months-long period where a couple is living apart but still legally married. This can lead to a lot of problems. Sometimes one spouse will refuse to make payments on their jointly-owned credit card. Or the spouse that typically pays the mortgage may stop paying. If you are not paying your debts during a separation but you are still legally married you are usually both going to suffer.
New debts might be on one spouse only
Some states have gotten fairer about new debts incurred during a separation. For example, if a couple separates and then the husband takes out a loan to buy a house with his new girlfriend, most people would say the soon-to-be-divorced wife should probably not be liable for that debt. Some courts may look at post-separation debts on a case-by-case basis. For example, running up the credit card to pay for marriage counseling might be considered a marital debt while a house for the new girlfriend is not.
The law in this area can change from place to place and depending on the type of debt, so be careful. If you have a joint credit card, for example, you may want to cancel that immediately to prevent your separated spouse from running up new debts that could be your responsibility.
A spouse could be required to pay
Some states can require a spouse to pay maintenance during a separation, and many spouses agree to it anyways. For example, in a single-breadwinner house, the breadwinner may have to pay the mortgage on the marital home even if he or she moves out. This can be frustrating because many divorcing spouses are not feeling particularly charitable towards their soon-to-be ex. The law in many states sees little difference between a separated spouse and a normal happy spouse, though.