Welcome to SI.
My belief is that you heal you, your SO heals your SO, and if you both do the work you need to do, you work together to heal your relationship. You can't do your SO's work, and he can't do yours. All fronts can be worked on a t the same time, but it's 3 different 'healings'.
My further belief s that your work consists of processing grief, fear, shame, and anger out of your body. A good IC can help.
You get through this by guiding yourself - express your feelings when it's safe to do so, hold them in when necessary. You may need some time alone to cry. You may want to pull over to the side of the road while driving or absent yourself rom your cubicle to scream or cry or just think.
The 2nd highest priority, IMO, after processing your feelings, is to figure out what you want. Do you really want this guy? If not, now is a good time to dump him. If you do want him, my reco is to observe him for several months to see if he consistently does his work - on himself and on your relationship. If he isn't consistent, he's not a good candidate for R.
Was this an ONS that happened on the trip? Is he on the trip in an official role? If so, he needs to brace himself for trouble. If it's an A that included a build-up and multiple meetings, be sure to ask why it's coming out now.
Here's some reading I suggest.
http://www.survivinginfidelity.com/healing_library/reconciliation/what-every-wayward-spouse-needs-to-know.asp - if this resonates with you, I suggest printing it off and giving the printout to your H as 'something you found on the web.' My reco: DO NOT tell your H about SI until you're sure he's on board for R.
http://www.survivinginfidelity.com/forums.asp?tid=361740&HL=14993 - serjr threads for newbies
Boundaries and Consequences 101:
Setting Healthy Boundaries:
Before You Say Reconcile:
The Simplified 180:
20/20 Hindsight: What I Wish I'd Done:
You can even R if you both do the necessary work. You can survive and thrive if you do your work, even if your WS does nothing. It's always OK to leave your WS behind.