The simple answer is that you do not have a personal liability unless you are part of the original agreement to borrow the money. However his debt can affect you. if he is maintaining payments on the debt and can do so until they are paid, probably nothing to be too concerned about. if however he is struggling with payments or has missed some, then this will or possible already has impacted on his credit record. The credit record should be held separately fro him and for you, but if you share and address this will show up when a search is carried out and MAY effect your ability to get credit in the future. this will be important if you were thinking of borrowing, or if you rent and need to move in the foreseeable future. Also if you own your property, he will acquire rights to it on your marriage and if he defaults on debt creditors could apply to have the debt charged against the property which is now a joint asset.
Get him to see someone for help with the debts, StepChange, Payplan or Citizens Advice so you know what the options are for dealing with them.