Would you tell the other partner?

I found out my husband was flirting with and sexting a female colleague a few weeks ago. We are working through it but reading their texts it is obvious that she initiated it all and always went further with it. I feel torn because I don’t want to be on a position where I cause drama as my partner works with this person, but if this woman’s fiancé had found out and I didn’t know, I’d want him to tell me. It makes me feel like I’m a bad person keeping this awful secret and not letting him know, despite never speaking to him or meeting him in my life. Has anyone else felt like this?