New Hampshire is an equitable division state, meaning when a court must decide the allocation of property and debt in a divorce, it will do so in an equitable way. There is some wiggle room with the term "equitable," but in general, there are a few things you can expect when it comes to some types of credit card debt.
One is that if you were the person to incur the debt before your marriage, it is unlikely that the court will require your spouse to carry some of it after the divorce. If you incurred it during marriage on a joint account, then a judge may be more likely to divide it. If you incurred it on a card in your name only during marriage, what happens to the debt is more clear-cut but can depend on factors such as why you used the card (for joint expenses, perhaps). In any case, here are some other ways that credit card debt can factor into a divorce.
In some cases, the amount of credit card debt (and other possible debts, such as medical bills) may lead to the divorcing parties deciding to file for bankruptcy. Doing so before the divorce is final often leads to a streamlined division process. Chapter 13 could be better if one of you wants to keep the house, while Chapter 7 might be preferable if erasing as much debt as possible is more important than keeping the house.
You can certainly file for bankruptcy after divorce instead of before, but doing so beforehand really does help clarify many issues.
Sometimes, one spouse opens a joint credit card account without the other spouse knowing. This account comes to light only during divorce proceedings and can be a nasty surprise. In fact, it can jeopardize the entire talks, sliding good-faith negotiations back several steps.
It is also possible that you knew about a joint account but assumed the both of you would stop using it after divorce proceedings began. However, your spouse could be using the card to rack up even more debt. It could also be that your spouse was responsible for paying the credit cards in full every month, only you discover he or she was paying the bare minimum. A lawyer can help you tackle these tough issues.