To the extent that your state permits, it's technically possible for there to be a legal separation order in place. But if a husband and wife live together as husband and wife... it shouldn't be too difficult to refute one spouse's claim that the couple was actually separated.

If your husband is worried about your debts, it should be possible for you to separate most (or perhaps all) of your financial obligations without separating. Depending upon your state, there may be a continued obligation for certain debts, such as those incurred for necessities of life (food, shelter, necessary medical care).