Hi there, you already have money missing so continue investigating that. Get bank statements, credit card statements, go through them. Does he have separate bank account or credit card? Look at money transfers to any accounts. Any unusual payments? Location of atm withdrawals? Do these tally with his location as far as you are aware?
So thats a start with money, next thing he needs is opportunity.. Does he socialise? Who with? Does he do work trips away from home? Does he socialise with work? Has he started working later? Any change in routine? Could you change your routine to meet him unexpectedly?
I'm not too tech savvy myself. Usual stuffs re: messages, emails, check for sent and deleted too, google maps maybe for location? Does he have a separate phone, pc for work and do you have access? Is there a possibility of a secret phone? Check what apps are on his phone and usage of each.
Most importantly listen to your gut instinct and try to keep a clear head. Journalling can help greatly with this (make sure he cant access the journal!)
As a previous poster said, if he doesnt think you suspect, he may be more complacent. Dont discuss with him or if there is something going on, he will try to cover his tracks.
Good luck. I hope your suspicions are unfounded