I dunno what to suggest to you, except that Al-Anon may help you to clear up your thinking. Was your marriage "good enough" to stick with while he was secretly drinking? If so, what has really changed, apart from the fact that you now know he isn't honest about it?
As Recovering noted, you HAVE been living with an active alcoholic all this time. Part of alcoholism involves hiding it. The hiding and lying about drinking is part and parcel of the alcoholism, it isn't that he takes great joy in hiding it from you.
Seems to me you can accept the fact that he will never admit his drinking, and continue as you have been (which I gather hasn't been so terrible), or you can decide you want something different and leave. It isn't a decision you must make immediately, though. I'd get a sponsor and start getting serious about your own recovery, and take some time to get your wits about you. You've been dealing with this for 16 years (whether you knew it or not), so there isn't exactly a rush about it. Take your time. More will be revealed.