As if you don't have enough to worry about being married to an alcoholic... add in finances... and it's another BIG worry. Yes, you are responsible for his debt. Debts and assets are 50/50 in most all states now.
Is is abnormal that he's secretive about the finances? YES. You should share that knowledge fully - NORMAL couples do.
Is a divorce expensive? YES. (mine was $25K - and I'm not a rich person... just middle class average person) We had a home, debt and it all got split... 50/50.
Should you have a lawyer? YES, if you have debt and property.
I'd advise you to take the blindfolds off, get informed as to what is going on. It's your right, and your responsibility. Having "trust" in an alcoholic is not wise. Don't put your faith in the thought he's being responsible. Protect yourself.
Never again will I EVER trust anyone with my security - emotionally or financially. "Once bitten, twice shy" you might say.