Download and install the free version (great program) of "Boss Everywhere":
http://www.bosseveryware.com/
It's a keylogger like Cache pointed to. Change the default settings to start a new log every 1024 bytes (not sure if that's the right amount, the free version will only record up to a fixed amount then start again, doesn't matter if you set it to make a new log every XXX bytes, check first), it's the demo limitation, but makes no difference once you change it, and make sure the "Tell users you are being recorded" flag isn't ticked.
One last thing, if you think he's cheating on you, he probably is, she was on me, so get ready for it.
But it's nice to have printed hard copies of their conversations to throw in their faces.