Infidelity Support Group
Any relationship in which one partner engages willfully in sexual relations with another outside of the partnership is considered to have experienced infidelity. This breach of trust is often traumatizing for the faithful partner as well as the relationship, and support is often needed to heal emotionally and to decide whether or not the relationship should continue after...
I agree that the Church would not consider this a marriage. I am certain your clergyperson would agree.
As for your children, all you are teaching them is that this is what marriage is and its ok for a husband to treat his wife like this and should they be in an abusive and/or neglectful situation they shouldn't stand up for themselves, they shouldn't make themselves overcome obstacles, and they should tolerate it.
Its a sad situation. I think you must consider IC.
Don't worry about being a good or bad Christian, as you won't be judged for outting him, because he is the one who is being bad. Outting him may seem unsavoury but it's the only thing that will stop him dead in his tracks, and hopefully send him back to Church where he can work on becoming a good Christian.
Just so you are aware, your children will mirror you in their relationships, so when you see your daughter or son in an abusive relationship, you'll know where it came from. I'm saying this so you are aware of the repercussion of his actions, and yours for doing nothing about it.
I wish you well.