I've been with DH for 15 years and met my best friend (let's call her R) 3 years ago. He likes her and is happy I've found such a good friend.
R and I have a running joke about 'the vault' which is how we refer to the things that are private discussions between us. She's a private person but completely open with me as she trusts me completely.
DH is aware there are things I don't tell him about her and he's started to take it personally. R split from her DH last year in really traumatic circumstances. DH knows the basics of what happened but not the details as I know she doesn't want anyone to know. He's said that I shouldn't be keeping any secrets from him but I've stressed they're not my secrets to keep.
In the same vein, I wouldn't discuss any of DH's personal issues with her and I've told him this.
YABU- you should tell your DH absolutely everything about your life and the people in it.
YANBU- your friends problems are not his business and she should be able to confide in you.