I consider IC my own personal time to go over my issues with a neutral party, so I only tell my husband the basics (e.g. we are going over my core shame and enmeshment issues, or I have homework to identify positive things about myself). He doesn't ask much about it anyway.

I was the same as GG.
There were multiple aspects to my IC: why I cheat, tools to overcome the behaviors, ending my relationship with my AP, and choosing to stay married and how to build they back up.
Both my IC and I didn't feel it would be beneficial to my husband to discuss intimate details of my affair and the angst I was experiencing ending it and moving forward.
I did share with him some tools she suggested in strengthening my marriage and I guess they worked- I'm still married.
I think you share what you feel comfortable sharing.
I hope you felt you could connect with the IC and it went well.

It went great. I usually read people pretty well when I meet them and I got a good vibe from her (DR). My wife has not asked about any details, she is very different from the BS that I have read about on here.

The doctor did recommend to meet with the both of us separately and together. That choice is up to my wife though. I just hope that I have the desire to stay married on the other side of this.

I agree with others that you should just share what you feel comfortable sharing, especially anything that you believe would be helpful for your partner to know.

I'm recently back in IC and am finding that I really need to be clear with my counselor about what my goal for counseling is. When I started about a year ago, my goal was to get support as I started the divorce process. I had come to that point several times in the past but had always chickened out or got overwhelmed with the logistical side. I was in IC for about 6 months and was able to get past the hard part - telling my H I wanted a divorce and moving out. Then my counselor went on maternity leave.

I just started up again and realized my counselor doesn't have a good idea of what I'm trying to get out of counseling now. She seems more judgemental than previously, and I wouldn't be surprised if post-partum hormones are impacting her ability to support me (I experienced this with both my pregnancies, a feeling of utter disgust when I thought about having cheated). I'm going to make sure that at my next session I'm clear with her what my goal is - to get support as I navigate my way through this non-traditional relationship in a way that is healthy for me.

Anyway, I think sometimes things will come out of your sessions that will be worth sharing, but you shouldn't feel obligated to share with your W unless you want to. The counseling is for YOU. And I hope your W will agree to meet with your doc with you and on her own. I think that could be very helpful.