I have severe mental illness, so does my husband. We have raised two children, our daughter and our son. Both are now in their 30's, both graduated suma cum laude from excellent universities and they are both in healthy marriages. Their lives are successful.
My daughter has had an anxiety disorder for which she takes medication and regularly sees a therapist. The anxiety disorder began when she was 3 years old. I immediately took her to a therapist, and she remained in therapy while she was growing up. (Definitely not something that was done for me when I was growing up, because my severely mentally ill mother was keeping too many secrets that she didn't want discovered. And of course, my mother would never seek treatment.)
Our kids were cherished, raised with an endless amount of unconditional love and support, clear boundaries. I was determined to break the cycle of abuse with which I grew up, which I did by remaining in mental health treatment while they were growing up. Fortunately, my husband and I agreed on parental styles, which was lucky.
So I will say that mental illness should not deter anyone from becoming a parent. What's important is to always put the child first. Meaning, be in touch with yourself and be in treatment to help your parenting be consistent and healthy.