*Should I continue with my marriage*?

[Carol]

Two wrongs don't make a right.
Your husband said that he would not retaliate against you but it looks like he did.
If he needed to talk to someone he could have went to a counselor.
At least you were honest and discussed it with him.
He sounds somewhat passive aggressive acting ok to your face then goes behind your back.
If he has done this to make you feel jealous it's a good way for him to destroy the marriage especially by telling her what happened.
He could have chose to talk to anybody else but deliberately picked her out.
He needs to cut off all communication with this woman and start focusing on the two of you.
I am sorry but that was just mean and you both need to talk about what is and is not acceptable for the relationship to continue.