Any debt in your sole name is entirely your responsibility; any in your husband's sole name is entirely his responsibility. If any of the debt is in both your names (for example, a joint current account or loan) then both of you are "jointly & severally liable". This means the creditor can pursue either of you for the full amount.
That is the legal position, but if you come to divorce the judge may take into consideration in the financial settlement which of you had and used the money (e.g. was there a loan in your name but your husband used the money?). The judge will look at this to help decide how any assets are to be divided, but his decision will not affect the legal position as far as the creditors are concerned.