He has a problem. Trust your gut. You wouldn't be posting here if you felt he had it under control or believed what he was telling you. Alcoholism looks different for everyone. There are binge drinkers (which he sounds like) who drink for months at a time then stop but they are still alcoholics.
Try to learn as much as you can about alcoholism for YOUR benefit but there is nothing you can do to make him change his pattern. He needs assistance, AA or some type of program to deal with this issue successfully.