My husband is a lend-a-hand kind of guy and if a coworker, male or female, said, "I need some help with something at my house" -- especially if the person had just moved, was new to the area, maybe didn't know other folks to ask -- he likely would want to help.
The big difference: He would tell me about it in advance. One, he'd just tell me, like he tells me other stuff. Two, he'd have to ask me -- not in the sense of needing any permission, but to check our schedules; see if I needed him to pick up our daughter somewhere or whatever. No big deal.
So your husband may truly have been helping out a coworker who told him "I need help but don't really know anyone... haven't done this before..." etc. But the part to worry about is the fact he did it three times and did not tell you until after the THIRD time. And you found out, as you say yourself, "by coincidence," which indicates to me he would not have told you at all had you not found out another way.
And that all adds up to this: He knew that telling you, "I'm going to Janie's at lunchtime tomorrow to look at this sink that's acting up" either would upset you or set off jealousy.
There are a couple of possible reasons behind it. One could be that he really was just innocently helping her out but still felt guilty about it. The other could be that he was afraid of your reaction. Is it possible that you've given him reason to hide things like this because in the past you've exhibited jealousies over innocent things? That would make him clam up (which makes things worse, I agree, but comes from a place of fear of your reaction, not from any real guilt that he's done wrong.)
Reread your own post: "Our marriage has remained pretty solid, but I just can't seem to shake the feelings of anger, hurt and betrayal." Do you see the contradiction there? You cannot have a solid marriage if there are unshakeable "feelings of anger, hurt and betrayal." Do you have any real ground for those feelings -- in other words has he actually cheated? Maybe, maybe not. But they are your feelings to own, and whether they stem from some real guilt on his part, or from oversensitivity and jealousy on your part, you and he need to work this out.
See a professional. You cannot claim a solid marriage when you simultaneously say you feel hurt and betrayed. Get a third party to help him articulate why he did not tell you about these visits and to help you understand what's going on with him and with yourself.
Your medical issues may be clouding your judgment here too. He may have feared that upsetting you by telling you he was helping this woman would make your health worse. You may be super-sensitive due to your illness -- you mention that you had to give up your career; could that loss be making it tougher on you to hear about his workplace friendships, successes, etc.?
I am not trying to be hard on you -- just saying that there is a lot more going on here than just a simple "He didn't tell me" situaition; there is the WHY behind his omission and you have serious illness in the mix.
You asked for suggestions. Mine is to see a couples counselor as soon as you can. Please be open to the idea that maybe your feelings about your illness factor into this and make you feel more insecure about any interactions he has with other women. He absolutely should not have gone to her home to help her without telling you, but his hiding it and your reactions and your condition -- all need to be untangled with help from an outsider who isn't caught up in emotions.