I'm the sole provider for the family (long story).
De-activate his cell phone and cancel the internet at your house.
You can still go "on-line" via your cell phone.
If he "goes to her", he "goes to her". At least you have more than "hearsay".
You also could make judicious use of a hidden voice activated recording device.
Is he bi-polar? Asking you to be "emotionally there for him" while conducting an electronic affair sure sounds crazy to me.
Just go along with crazy acting non-suspicious while you accumulate the data you need to undertake church discipline. His boss sounds like a coward so you probably need to take it to the church board or other governing body. His father and mother, if Christian, should also be a good source for support.
The internet is 90% complaining and entitlement and I hate it because I deserve better!