If there are joint credit cards or other joint debts then the spouse that did not file would still owe the debts. Otherwise, if the debt is just in the name of the spouse filing for bankruptcy, creditors would not even know the other spouse exists.
Bankruptcy law allows a married couple to file together, but they are not required to do so. Either husband or wife can file by themselves, or not file, or even file two different types of bankruptcy at the same time. Your spouse may not need to file bankruptcy at all or one spouse may need to file a chapter 7 and the other may need to file a chapter 13. You are allowed to file a bankruptcy by yourself and wipe out the debts you can discharge. You have several options!