He does reasonable cause for suspecting something is going on and just needs to have information available to aid him in making decisions about some unusual behavior.
Then you're being coy with us about details that would really help you get good answers about this situation. And most likely, these answers will not be technological, but rather revolve around (a) seeking marriage/psychological/etc. counseling, (b) contacting law enforcement, or (c) just talking to his wife/children about what's going on.
The biggest favor you can do for this guy is to not indulge his creepy need to spy on his household. It's passive aggressiveness at its worst, when he really just needs to confront whatever issue this is head-on.