Rose,
The above posts are spot on. Your husband does not have a problem with his drinking, you do. So it's not his problem to fix, its yours . What are you going to do about your problem?
You know he is drinking and lying, as that is basic 101 when dealing with an addict. We validate that for you; as they make you feel like you are "crazy". Now that you see who he really is, what is it that Rose wants? I see that you don't want a divorce, as none of us who come here did/do. We come to these forums to find out how to get our addict sober, and live happily ever after. You will see, when loving an addict, there are very few happily ever afters.
I would keep going to the therapist, hitting alanon meetings, keep reading all over this forum, and maybe even hit an open aa meeting. Education is power. Take this time and realize what you are up against. Then make the decision that you feel is best for you. We are all here for you, keep posting and asking questions.
Sending hugs to you..