I wrote a detailed response, but malfunctioned when tried to post it.

bottom line, you need to get counseling on this (a marriage or relationship counselor) to get to the bottom of you (and his) understanding of INTERNET ADDICTION and to determine the extent of his obsessive on-line social behavor with other women and what its all about and if he understands and cares about the effect it has on you .. and once he does grasp it all, how he feels and reacts to get this problem resolved and about YOUR feelings and needs in this regard.

His actions could be quite innocent (at least at this point) and just a habit that has become an obsession ... and it might not mean he does not love or appreciate you.  But, sounds like its an addiction for him and he has to come to grips with the reality of that and the reality of the IMPACT it has on you and why he needs to break that addiction.  

Perhaps he would let you sit and watch his chats?  Some couples do that and both laugh or enjoy it, even if they don't know you are watching too.  Maybe he will feel that you are overstepping by even suggesting that; if so he is looking at it all from a very self centered point of view and is pretty foolish (or indifferent) not to see how it affects you.

Best wishes getting his internet compulsion under control, it can be a real challenge for some who are really addicted .. and he was doing it BEFORE you moved in and could be very addicted to this social behavior on line.

Rob