This is an interesting and precarious situation.
I understand that you can have a normal and healthy friendship with someone of the opposite sex. I guess my concern is that this is something that is not benefiting your marriage.
We have managed to stay friends and even bring kids together for playdates, without our spouses.
While I'm not good friends with OBS, my wife and I are friends with another couple that has a fWW and another BH. I have gotten together with just the wife of the couple for playdates with the kids, and actually have also spent one-on-one time together. I have mentioned this in other threads, and some folks on this forum have warned me that she seems to be trying to wedge herself between me and my wife (honestly ever since my JFO thread nearly 3 years ago).
I think she is a good friend of the marriage. This is because we have an open dialog about her A and my wife's A, and I think of it as a way to get perspective on the A without the inherent conflict of talking to your own WS about it. We have set careful boundaries in terms of not actually complaining about either of our spouses.
Interestingly, she helped take care of my kids alone while my wife was on travel and I needed to go see my father as he passed away.
I consider her to be a very good friend. I understand that these circumstances aren't the same as yours, but I'm just giving an example of a close opposite sex friendship I have.
That said, if my wife were to say, "TIF, I don't like that you and fWW friend spend time together without me." I would drop any such activities and set that boundary. At the end of the day, I'm married to my wife and she has to come first. If my friend is causing my wife grief, then she isn't really a friend of the marriage even if I feel like she is helping me in the marriage.
However, it has been tricky to navigate - naturally he is not a fan of my WH and voiced his concern about my marriage ("twice a cheater, ...") a few months ago.
I think,since he is a good friend,you should consider what he said. Your husband is a serial cheater. It concerns me that you said you are working on your marriage. Your marriage didn't cheat. Your husband did.
I think its natural that your good friend is asking the questions he is. It's also ok if you don't want to discuss things with him. It's ok to tell him any discussion about your husband is off limits.
I more or less, agree with Hellfire on this topic. Spending one on one time and discussing your relationship and recovery in detail can be problematic if he isn't going to be supporting you in R. You shouldn't have to defend your decision to him, and that's how you could set that boundary. "I have chose R, and if that ever changes, I'll let you know, but until then, I'd prefer you support my decision. If you can't support that decision, you can either stay quiet about it, or we can stop hanging out."
I would also ask myself a few questions if I were you, just to keep yourself honest (no need to answer here, they are questions for yourself).
1) Do I find OBS attractive?
2) Do I think (or know) OBS finds me attractive?
3) If my marriage were to end (for whatever reason) would I consider OBS a good person to date?
Even if everything is "above boards" right now, you could see how answers to those questions could make the friendship at least appear in poor taste. It would also be understandable as to why your WH wouldn't approve of this friendship, even without the fact that OBS has every reason to dislike your husband.
For example, if your H left you and you started dating OBS, it would be very hard to prove a claim you haven't already had an A with OBS.