Living with someone who is chronically ill is extremely stressful. And it's miserable being inside the head of depression. I completely understand your husband's viewpoint because I have been there - short of the suicidal thoughts that is. But I certainly sat around, barely accomplishing anything, and holding the viewpoint that this won't work and that won't happen and so on. I also know the feeling of the medications not working. Anti-depressants can't do everything - they can sometimes take away the very low lows, but they don't restore the highs, which means that there is often a lot of joy missing. When there's no joy, it's hard to have hope.
I think your husband made a huge mistake going off his meds. Medications need to be cut back slowly, and he's made no effort to find another one. He did this without a doctor's supervision. It takes a few months for them to get out of your system, which is probably why you didn't notice anything for a few weeks and now he's engaging in this really dark talk again. You're going to see a therapist, which is good, but it's not for a few weeks, which is bad. I was depressed for many many years (undiagnosed), and finally it was a relief to have a diagnosis and realize I wasn't responsible for just being moody and lazy. I tried a couple of medications, found one that stabilized me, and stayed there for years. I also did therapy, both individual and couples work.
About 6 years ago I started a phenomenal supplement (just trying not to get sick all the time and not have allergies) but found I felt so much better over time. I found I had more energy, was able to go to the gym (which made a lot of things better), and over time I found my mood lifting because the chemical imbalance that caused the depression was eventually restored. Working with my doctor (that's important) who loved the results she was seeing both emotionally and medically (lab tests much better), I weaned off the meds and have been medication-free for quite some time now, with no recurrence.
My husband's brother was ill as well, and suicidal. He went off his meds because he was worried about side effects (which he wasn't having - he just read about them), and within a few months, he took his own life. His wife had heard him talk like this for a long time, and had interrupted several attempts. Finally he was successful. I tell you this because I want you to take these musings seriously. He should have some sort of emergency intervention - please call his physician immediately.
I disagree with the statement below that people with depression can be self-centered. It LOOKS like that but it's not. It's a chemical imbalance, a medical condition. It requires treatment, either therapy or medication or both, and nutritional support on top of that. Once the crisis is averted, a long-term program can be selected. For me, nutritional supplementation works, but even so, I have to stay with it.
It's important that you realize you are not causing it. However, his lack of sleep is not a good addition to the situation and could be making it a lot worse. I think it might be time to make a change in terms of the younger daughter being in your room all the time and not sleeping through the night because she wants to nurse. A child that age needs her rest. Irregular sleeping patterns can contribute to, or be the sign of, depression and other forms of mental illness. Deep sleep, REM sleep, is important for brain function. That goes for her, and for you, and for your husband. So I think you've got to get this child on an all-night sleep regimen, starting yesterday.
If your husband needs to be hospitalized, do it. If your daughter needs a few sleepless nights to learn to self-soothe, fine. And if you need to be a little less of the person everyone leans on to get through their issues, that's a good position for you to take.
Please reach out to the physician for immediate help, see if the therapist can take you sooner, and get some support and advice from NAMI (National Association for Mental Illness).
Good luck - there is hope and I'm living proof of it.