I really feel for you, especially in your current state.
Sadly, modern technology has increased the ability and of course numbers, of people who 'cyber-cheat', and as you point out, the fact that 'nothing has happened yet' does not alter the fact that systems were in place for that last step to be taken.
You need to have a serious talk with your husband about his future, and yours, and yours as a couple, if there is one.
If he decides to stay, then you need to seriously make him suffer for this - he dserves it, and you deserve to return some of the pain he has inflicted.
That said - he cannot pay for ever and a day, and there will have to be a time when you both put this behind you, and move on, and that means no bringing it up in a row, or constant fretting from you. If you cannot move on, then your marriage os over - but that is for the future.
For now, take it day to day, and concentrate on you and your children - and let him feel as guilty as possible.
When you feel yourself healing - if indeed you do - will be the time to talk over what has happened and where you both go from here.
For now, try to stay focused on baby, and park this whole sorry business until you can deal with it properly.
If you need support, there are loads of people on here to look after you - technology does have its good side as well!
Thinking of you.
A x