We are talk in about trust that has been betrayed, so of course you don’t trust him. That Trust is broken and the onus is on him to fix it. If that requires him sharing all passwords and phones and accounts with you, he should gladly do it. Peter already recently wrote an article about Social Media and infidelity and one of the first rules he recommends couples to follow, in order to not fall into the cheating trap, is precisely this, to share all passwords and accounts. Doesn’t mean you have to log in hourly in everything to see what he is doing but it will make him realize that at ANY POINT you may do that and therefore he should not be in an incriminating situation.
DH and I have shared all passwords and even bank accounts since before we were even married or engaged. When lines we crossed, we would heighten the limits for the other in order to “reset” things there were times when we needed to establish curfews because “some” of us were forgetting to check the time when there was a company event or a friend’s birthday party…we accepted these terms because it was more important to gave things right with one another than to have an extra beer with the CEO,
So, as far as I am concerned, it is perfectly reasonable for you to demand access to whatever it may be that enabled the betrayal in the first place, or that may enable it to happen again. Simply tell him that you can not, for obvious reasons, be at ease without this transperancy in your marriage. And, obviously, be ready to reciprocate because double standards are never healthy in a relationship.
The only thing that perhaps you can be more indulgent with…coming from the outside I don’t know for sure which way I’d go…but, perhaps give him time to “think” about it .I.e, delete, block, remove whatever evidence may be accessible. I don’t think it’d do you any good to find things in his web browser or his email or his messaging history with the details. If you think you can handle it, assume that risk, if you’d rather not know., then make it as of “tomorrow” so that he has time to clean things up. If the Internet wasn’t involved, than this is a non-issue