Cutting back on his drinking, is not a step towards recovery. He is simply trying to pacify you.
My AH did this over and over, usually precipitated by a drinking incident, usually where he picked a big fight. Currently, he says he has not been drinking or smoking pot as much. The pacification never lasts. Addicts have to prove they are in control of their addiction, but without recovery the addiction controls them. AH's use of his DOC always cycles up, even after a period of not using that much.