Followed by calls to check his phone (wait til he's asleep then use his fingerprint to access it), put a tracker in his car and hire a private investigator. He's following the cheater's script, OP, he's probably got another family or at the very least another woman. Get your ducks in a row and hire a shit hot solicitor.
In fact the husband in this scenario is absolutely 100% over the moon that they are having a baby because they had already suffered a pregnancy loss, then he'd been through treatment for testicular cancer. The cancer is now in remission and he wants the whole world to know how much he loves his wife and cannot wait to be a dad.

