The more time you spend reading here, you'll see that most cheaters don't nearly tell the honest truth on D Day. Quite honestly, your husband's story is like all the rest of them when they get caught - they ALL claim it was a one night stand - just a random one time thing. You'll find over the next weeks/months that this is probably not true.
Do some reading in the Healing Library (the yellow bar on the left) and do tons of reading here on the boards. The info you get will be invaluable - and more than likely keep you from being steamrolled from the actual truth.
Good luck to you.
I'm so sorry. This is not what you will want to hear, but it is too early to really choose to stay, because there is just no way that you know the full truth yet, and you can't commit to working on something until you know what you're dealing with. How likely is it that he has one ONS and the condom just happens to break and he just happens to get an STD?
It is so hard to lose the certainty about your relationship, but I think you are trying to cling to it by accepting this version of reality. Please consider whether you really are getting the full truth or whether (as is almost always the case) there is more to the story.
In the meantime take care of yourself and know that no matter what you will survive this.
Investigate things. His email, phone records, credit card records and bank statements. Look for inconsistencies and discrepancies. Check his texts, look at his computer.
It is too early to make the decision to stay in the relationship, because you don't know the full story. That doesn't mean you have to leave either-just get to the truth before you decide.
I've found the key to happiness: Stay away from assholes.
Do you wonder, would he have confessed the ONS if he hadn't contracted an STD?? Is this the first time, really?? Investigate. Give yourself plenty of time to think of the possibilities of what you don't know. You're probably still in shock.
Hang in there.
Gently, I tend to agree with the other posters that there is more to your husband's story than he is telling you.
Please read the articles in the healing library, they will help you begin to process the pain.