Visit the cc's website and get detailed info on the transaction. That should list the verizon account number that you can take to them and ask fro a detailed bill which will list phone numbers and calls. They have access to text messages too but that takes months to get. Odds are Vz wont even talk to you unless you're on the account but good luck.
Why do you need the extra proof? You said 'who he's now cheating with' which to me implies he's done this before. Are you going to find out who it is and fight with her? She's not the problem; he's the one being deceitful.