R.,
I would be upset too, I do not think a husband should have friendships with other women unless she's married and the real friendship is between the two men and the two women. Next thing that will be said is, "I can't talk to you like I talk to her, or she doesn't have anyone to talk too..." She needs to find a single man if she's not married, which I'm sure your husband wouldn't like it if the shoe was on the other foot. You are your husband's best friend, and he should be able to talk to you about everything, and just because he's being completely honest with you, don't make the excuse that it's okay to do then. You are his WIFE. This woman might be a nice person, I wouldn't invite her over, I seriously don't think she needs to be apart of his life at all, only at work if really needed. I'm telling you, this is a door that shouldn't open. You are making excuses because he's using work, I understand it's important for your husband to talk to someone at work, but not a female. I'm sorry, but I only see problems with this relationship. I'm sure your husband is a great man, but even the best of men can end up cheating and not mean too.
And don't think for a minute it's bad to be jealous, there is a line of being too jealous, but you are his wife and he doesn't need any other woman to be that close too. I would tell him to stop, that you don't like how it makes you feel.
If anything is work related it can stay right there at work, there doesn't need to be emails exchange or telephone calls outside of work. She should respect you as his wife and even if she feels she's not doing anything wrong, she's a woman and how would she feel if some female was going to lunch with her husband.
This is my opinion....