There IS no understanding an addict (and your husband has TWO addictions -- alcohol, and the rush of an affair). The only thing to "understand" about an addict is that they will do or say ANYTHING to keep fueling their addiction, and conversely, they will react STRONGLY to anyone who tries to DISRUPT the source of their addiction.
I haven't read your sitch, but considering how long you say this has been going on, I'd suggest you do whatever you need to do start protecting you and your children -- emotionally, legally -- and STOP trying to "understand" your husband's behavior.
There is a time to stand in loving support of the addict. And then there comes a time to say "I will not let you pull me underwater also -- you need help" and to leave. Only you know when that time is.
btw, I am the child (and grandchild, and nephew) of an alcoholic, and I do sympathize with your situation.
