@miserablysad,
IMHO, you're right to move out as he lied and schemed to meet up with the woman. Kudos go to you for contacting this woman as well as confront him on this. You clearly are not acting as a victim. Continue with your plan to move out. He gambled on your trust and he lost.
However,
only you can determine what the right course of action is for your marriage's future. Filing for divorce shows you REALLY mean business. Getting the divorce granted ...well, another issue entirely. However, thatr's a long way down the road. Take time and think about how far you want to go?
What were things like in marriage prior to the "date"? How long are you married? How old are you both? Any kids? Did he make you happy prior to this? Did he and this woman make love - or would you only be guessing about this? Was he trying to fool her, too?
Perhaps you might let the dust settle and see whether or not he is truly contrite and behaves while you are separated? How will you be able to verify he was well behaved? Trust might be hard to validate.
If he lied and cheated after you first caught him making the date etc., well? Many would find it it hard to EVER trust him again. If after an extended period of time (your timeframe), he's mended his wicked ways and goes to marriage counselor with you -- perhaps you could reconsider and cancel the divorce papers.
You need to determine what scenario works for you and what is both in your heart and mind.