Well....he can't both be 'done drinking' and 'drinking heavily and daily'.
So, I would definitely watch his actions. I don't know what to say about your 15 yo son. I suppose if it were me, I think I would just try not to future trip about what your husband may or may not say to your son. You may have 2 options here. 1) wait and watch and see whether or not your husband says anything to your son; 2) talk to your son yourself "Your Dad told me today that he is through with alcohol. I'm telling you because I thought you should know. Although it would be great if it's true, I'm taking a wait and see approach."
I hope your husband will somehow find his way to real recovery. Take care of you and your son!