dear merito,
I’m typing on the basis that he DID do something wrong (you’ll have to find that out by honest talk). I disagree with the generic notion that if you stick around, you’ll be deemed as a close-one-eye wife and your husband may further take you for granted. Would you consider the option of laying facts on the table with your husband, and seek his cooperation in making this marriage and new family work?
Is it out of his character to behave like this? Men and women fall into temptations, what was done once repeated again becomes a habit and a downward spiral into vice and sin. So if your husband has always been an honest guy and this comes along, he may just need someone’s help to pull him out of the trap.
It’s not use throwing the topic at him, catch him unaware and then… what next? Even before you start talking, prepare your response if his answer is a ‘yes’. If you are able to forgive and continue in this marriage, it’s not closing one eye. It’s making your stand to him that unfaithfulness is not acceptable to this marriage, but you are willing to seal this as a past and need his help to work with you.
As much as it hurts, it is not worth for the marriage to be broken up and a fatherless child to be raised, just because of some unknown parties who came into the picture (who can’t even care less what they did to your family).
You mentioned he’s very happy about the baby? That’s a great sign he wants you and this family. you shall decide if the man is worth giving a chance.
but be prepared to apologise for breaking into his account if his answer is genuinely 'no' though...