Could they be text messages that he is deleting? You might try to to look up the name for that number. Sometimes it works. Also it might be a signal from someone else. Sorry I am being all negative just my BS side talking. Hope it's nothing but it doesn't sound good. Your H should not be keeping things private from you. And IMHO getting serious about the IC or MC with Penny is just an excuse for the email account.

Wish you the best and take care.