I am able to approach this question from several different perspectives.
I myself am a partner with mental illness. I have bipolar disorder — and all the accompanying depression and anxiety issues that come with it. I was diagnosed when I had basically hit rock bottom, but I worked very hard to become a functional person again. I learned how to cope with, manage, and monitor my condition. I take medication daily and see a therapist and psychiatrist regularly. My issues still pop up — recently I found myself sliding into a depression, which I consulted with my doctors about right away and took steps to remedy; I also feel that a few times my anxiety has interfered with my relationship in a negative way. But overall, these things have been minor, and I always take responsibility and try to improve things. I want to be the best partner I can be for my fiance, and that means making sure I take care of myself.
I have had two very different experiences with partners who were also mentally ill.
My ex-boyfriend had depression, anxiety, and ADHD. He didn’t manage his illnesses well, and basically did all the wrong things. No matter how many times I tried to get him into therapy, he was very resistant, and when he did go, he didn’t implement any of the suggestions. He didn’t take his meds regularly. Addiction issues began to surface — alcohol, cigarettes, prescription meds (both his own prescriptions and other peoples’). He couldn’t hold down a job. He was not able to be an equal partner to me, and while I thought I was helping him at first, I ended up just enabling him. You can’t fix someone if they don’t want to fix themselves.
My fiance now also has had mental health struggles — depression, anxiety, and PTSD from his time in the military. However, he did the work he needed to do to manage his issues, much like I did. He holds down a full-time job as well as a side job, and is able to handle responsibility. His issues pop up sometimes too — he gets night terrors occasionally, he gets anxious sometimes, and just yesterday, he mentioned that he feels he might be in a mild depression. He doesn’t currently take medication, but is toying with the idea of doing so temporarily to get past this. His approach to our relationship is similar to mine: he wants to be the best partner possible, and so he monitors himself and takes responsibility for his issues when he needs to. This relationship has by far been the easiest relationship I have ever been in.
A relationship with a person who struggles with anxiety and depression can be very fulfilling, and most of the time it shouldn’t be any different from a “normal” relationship. But this is only the case if your partner is diligent about managing their condition. He should NOT be relying on you to cure or fix him, because that is not your job. Your role is simply to be supportive, compassionate, patient, and try to understand what he is going through when issues arise. You also can’t take it personally if he becomes depressed when he is with you; even though he may be very happy with your relationship, there may be other life factors weighing him down, or it might just be a chemical imbalance.
Overall, I’m clearly biased, but I don’t think his having depression and anxiety should dissuade you from dating this guy, provided he is taking the appropriate measures to manage it.