Be carefull on how much "looking into" you do on him. He may be cheating,, in which case you would be justified. But if hes not cheating, and he discovers that you have been going through his cell phone/emails/bank statements/etc/etc/etc. There will be alot of anger. Not only will you have completely violated his privacy, but you will have showed how there is a complete lack of trust.
Honestly..I would just talk to him, it's the best option, let him know that the appearance he is giving off is hurting you. You don't need to worry about "warning him" or "giving him a heads up"...this isn't an episode of Magnum PI, this is a relationship. Talk to him, try and work things out. Sometimes we do things that we feel are harmless, and we don't realize we are hurting our spouses until they point it out.
Skeeter
Skeeter, I hope you NEVER go through something like this because once you have had your spouse cheat, you will totally understand the advice I have given. There is every reason to think the things I have said IF he is really cheating.
I kind of envy people who have no idea about things like this. Honestly, now that I have seen this side of a relationship, I don't know how to get back into one.