Addicts are accomplished liars...they will say anything and everything to get their fix. SA's are not different.
You have the right to be safe and secure in your marriage. You have a right to set and expect boundaires on moral sexual behavior. There must be - and this is crucial - consequences for his behavior when he exceeds those boundaries. Those boundaries are up to you. If he was owning up to the problem and actively in recovery, that is one thing. But a hub in denial - you may as well be talking to a wall.
You have the right - and if you have kids, the obligation - to be the protectress of your family. His actions are a direct threat to you family. The question soon becomes: How much of this are you willing to take before you do something?
You may want to look at the website http://www.marriedtoasexaddict.com
for some support and resources. Just be careful there; there is some great advice and heart-wrenching stories there, but there is a lot of anger and hostility there....understandably so.