There is no "normal" in life. What you can say is does this make you comfortable or not? And since you are asking if it is normal, I am assuming you are not happy about it. This may be causing some stress in your relationship and I am going to answer 100% honest here. If he were confiding in a man would you feel threatened? You just experienced a recent loss, and your hormones are all over the place which can make you a little more sensitive to his actions. Is he talking to this "woman" behind your back? Are they discussing the loss? Perhaps he is talking to her to get advice on your relationship. I have many friends that are men, and I have confided in them from time to time regarding Anthony and I do not think Anthony would feel threatened by it. BUT and this is a big BUT...if you have expressed your dislike for their friendship and he continues to confide in her, you have to start to ask yourself, "Am I making myself unapproachable?" Does he feel like he can not talk to you about certain things and so he talks to her?
Men are not as complicated as we make them seem, in fact they are a simple breed. I am probably offending some men with that statement, but its true guys. YOU are not a science project. You do things usually for no extra reasons. It is kind of like a what you see is what you get. I think he may talk to this woman because she is giving the impression she is "One of the guys". Men are usually the victims to women who do not know how to back off. My advice to you is to just let him know how you feel (and I am assuming you have) and let him know that because of your recent loss you are vulnerable and you need to feel that YOU are the one and only person he wants to confide in. You need to get to the source of why he is talking so often with her. I think once you have gotten to the core of it the solution will be right in front of you.
It is normal for husbands to talk to their friends about stuff. It is NOT normal for them to do it with people whom you are uncomfortable with. Hope I was able to help...
But hey, that's just "My Two Cents"