I think your situation is very different from whatdidIdo's. If, if, IF you are in a committed relationship with your spouse, and neither is currently wayward and you're in the "no-contact/transparency" period, then yes, absolutely -- HARD-CORE HONESTY and I think you would have to tell him about the calls.
Your case is certainly different, and this is what I would recommend:
1) DON'T tell your husband -- he'll only use it for some false sense of moral equivalency, and the fact is that you've done nothing inappropriate anyway.
2) In fact, the next time your husband starts giving you the third degree about your comings and goings (and I believe I may have suggested this to you already?), do NOT engage him on the subject. Simply say "You have no right to expect to get my itinerary from me right now. You left me. If you need to know something about the kids, I'm happy to oblige. Now please don't interrogate me in this manner again, because it's incredibly insulting and I won't tolerate it. Besides, it's paranoid, and -- frankly -- not very attractive." (ooh, us men HATE to get that one!!!)
3) DO tell the OM, "please don't call or text me. I know you're just being nice, and it's all innocent, but I'm trying to work thru a difficult situation with my husband right now, and I just don't need for him to have anything on me that might give ANY appearance of impropriety. It's best for us to keep our communication at work only, and ABOUT work only, and I hope you can respect that."
Short version: let your husband twist in the wind a little, but DO let your friend know that he can't contact you outside of work.