Yes, it's still cheating, obviously -- he's still married to you.
You need to set (and learn to enforce) some boundaries here, JL. It's not emotionally healthy for you -- OR your kids! -- to have your husband's infidelity rubbed in your face on a weekly basis.
Have you told him that the current arrangement is unacceptable? Do you have any family who can help you out logistically and financially, so you can do what you need to do here?