Look hun, you have to have a serious talk with your hubby. It is not right for a man to talk about his personal issues with another woman. You are the wife and therefore if he has any worries or so he should tell you, not her.
Try to set things straight because getting too intimate/close with another woman and talking to her about personal issues may be the end of your marriage. Don't let this happen. Tell him to stop talking to her because you just don't feel comfortable with it. One thing I always tell my partner is to respect my feelings in the sense that if he is doing something I'm not ok with then he should immediately stop it......I don't care if it's just a friendship..if I don't like it then I'll go with my instinct.
Just ask him how he would feel if you guys switched places: You talking to a guy about things that should only be discused between couples, not friends and maybe he'll understand your point of view.
Good luck
I think that if it bothers you that much then you should tell him that you would appreciate it if he cut off the friendship with her. That you don't feel comfortable with him talking to another woman about the problems that you are having in your marriage or any other issues that may be happening. If he cares about your feelings than he will do it. I know that I would have the same feelings you do if it were my fiance talking to another woman about emotional issues.