Visit the link in my signature and spend a lot of time there, there is also a great board over there for these types of things too, but read all of the info and the infidelity section.
After you are done spending time there, schedule yourself for the Marriage Builders weekend they host (which is followed by a 12-week course in which you two will complete assignments designed to repair your damaged relationship).
Get yourself into individual counseling; insurance will cover it. Encourage her to do the same. Once you have been in individual counseling for awhile, have your docter diagnose you with adjustment disorder so that you can qualify for couples counseling together on your insurance.
In addition to reading the MB site, pick up a couple books right now: Surviving an Affair, Dr. William F. Hartley; Relationship Rescue, Dr. Phil; Love Must be Tough, James Dobson.
Spend a lot of extra time with your kids and do not get into fights out of pain and the desire to inflict pain. Give without expecting back. If you want to keep it together, that is your choice, but it is very hard and you will both need to put in the work. Marriage Builders is fucking fantastic for this.
P.S. Do not feel odd about wanting to keep your relationship together. This happens most of the time in these situations. It is not unnatural.