I've sort of been in a similar situation with my other half.
He did something before we got together that I found out about after we'd been together for about 8 months (and had lived together for 2 - he too asked me to move in with him, after 6 months).
It was one of those things that gave me that really sick feeling too and took a long time for us to move forward from. and we argued for ages. I really don't think you can just pretend it didnt happen and not talk about it. I also think if it is an addicition, he (and you) need help understanding why he did it. However, I suspect he's v embarrassed about it too.
My bf and I ended up going to Relate over it for a few months which perhaps you and your other half ought to think about. I was quite sad about the idea because we'd only been together for 18 months at the time and the idea of needing therapy after such a short period of time was quite depressing - but it was the right thing to do.
We went to sessions together and talked about how we were both feeling about these things, and I think it went a long way to getting us through it. At the end of the day, I thought the relationship was worth giving it a go
I still think about what happened occasionally and it does make me feel a little funny for a few seconds but not sick in the stomach anymore.
Feeling for you. I know its tough but take comfort in that he obviosuly feels bad about it, knows it is wrong and wants to change. He has to understand that this isn't just his issue now though - it affects you and if you want to talk about it, you have that right.