The problem is that your husband is most likely an alcoholic and they cannot lighten up when it comes to drinking. They might do it for a short time, but it's always temporary. An alcoholic simply cannot drink at all because they cannot control their drinking and will always abuse it. That is the number one thing you must understand when you are dealing with an alcoholic.
It seems as though he is headed towards liver problems from his drinking. It starts out as a fatty liver but if the drinking doesn't stop, it can progress to cirrhosis and liver failure. I doubt very much he will "lighten up" for very long, but if a person has a fatty liver, they should not be drinking alcohol at all, not even smaller amounts. The doctor is right that he must stop drinking all alcohol.
Cirrhosis is a really bad disease. It's a slow and miserable way to die. Look it up in Wikipedia and you can read all about it. I know because I had it from an autoimmune disease and had to get a transplant. No matter what causes cirrhosis, the disease pretty much acts the same with everyone. This is a wake up call for your husband. If he lets this fatty liver progress to more serious disease and enough damage is done to his liver, nothing is going to save him except a transplant. An active alcoholic would never qualify for one.