Should my husband allow me access to his passwords for email/facebook accounts?

[PunkWithValues]

He doesn't deserve your trust. He lost that privilege when he began acting in distrustful ways and being secretive.

Checking out porn, giving you trickle truth about it?
TWO trips with pals (to vegas no less), and none w/you?
Drug use?

People who have nothing to hide, hide nothing.

Snoop his stuff. Now.
Check his phone when he's in bed.
Check his internet history usage. if he's been online and the history shows not as much use as you've seen click-throughs, he's either deleting history or using private browsing.
Find a way into his emails, etc. Android and IPhones have auto access apps. Check for dating apps on his phone, too.
Have friends help you by checking up on him. Is he where he said he would be, with the person he said he'd be with? If you can, you borrow a car to see what he's up to.

Also, Desktopshark has both phone and computer keyloggers and trackers...free and paid versions. Check into it (but delete yoru own browsing history.)

While you snoop, ask him nothing else about it. Just do it. No warning, nothing.

He is lying while you are in counseling. Based on that alone, I'd prepare to leave after giving him "everything he wants" emotionally (certainly not financially) for one month. Then leave and go totally no contact (set up your own financial reserves first though.)

Good luck to you!