I think going to an Al Anon meeting would be a great idea. Not only will you get support, you get ideas as how to cope with your husband. You will see a huge variety of folks that have a huge variety of reasons they are there. Just there is a huge variety of reasons someone ever turns to alcohol. And a huge variety of reasons they hide it.
I can say the most COMMON reason they hide their alcohol use is because they are ashamed. If your husband is in one of the most stressful professions there is with the high expectations this sets up a precedent that he has to be strong and tough and cannot show his weaknesses. I don't know what the divorce rate is among cops...but just being a cop without substance abuse involved can be a strain on spouses and families. I think being in a relationship with anyone who has a stressful job would be a strain. My husband was a probation officer for a long time and even though he didn't see as much violence, he saw a lot of bad stuff and managed to bring some of negative stuff home with him. It hasn't been a cake walk.
The simple fact that he feels shame about his alcohol use tells me he is a good man who knows it is wrong, but a desperate man who reached for the bottle when he should have been reaching for other help and support. It can be lonely place when you do not feel people understand and will condemn you if you reveal you alcohol use. In my experience the reaction you get from people varies. Some don't care if you drink, because they do too and others would shun you while not really offering the support you need.
It's frustrating when you see a loved one struggling, hurting, needing help and you just cannot seem to help them. It's frustrating when people need to change, say they will change and maybe change for awhile, but revert back to old habits. I've come to realize that habits are hard to change, but not impossible, whatever the bad habit happens to be. And if the addict has enablers in their life, even harder. Once someone gets clean and sober, there is always that fear of relapse and how disappointed the addict is with theirself and how disappointed their loved ones are.