I believe that when someone is hiding drinking vodka they are doing it because they think it doesn't have a smell and they are doing it because they know they are drinking too much and that they don't want others to know just how much. It is a worry for them, even if they don't admit it. My closet drinking AH husband started out just like yours.
Regardless, it has become a problem for you.
Get comfortable and read lots here. I also attend Alanon. It is for the families and friends of alcoholics. It's really great to have face to face support and you learn lots on how to help you. It can get better whether or not the alcoholic continues to drink.
You might as well stop snooping or nagging. In my case it just made him better at sneaking and acting sober. (Although mine drinks daily, I haven't actually seen him drink for YEARS.) You did not cause his drinking and more importantly YOU can't control it and YOU cannot cure it. And you might as well accept that if he is going to continue to drink, he will lie. They have to lie to protect the drinking. This sounds cold, but I think you might as well put your energies into YOU.
Thinking of you.