Ohh dear sounds like you are all having a very tough time.
Having 3 children all under 4 is bound to be exhausting and hard work so you are doing a much better job than you probably feel you are.
Is there anything in particular that cause DH's 'meltdown'? What aspects of parenting does he struggle with in particular? Or is it just the grind of it all?
I only have 2 children but I can relate to the 'it'll get better when...' I have been saying this since DS2 was born 19 months ago. That's not to say it hasn't got easier along the way. It must have done. But it's still hard. (Sorry, probably not what you want to hear but you already know this having survived having 2 already!)
I can't offer any advice as such but I can tell you that there is light at the end of the tunnel. It might just be a very long tunnel
but you will get through it.
Is the the baby waking to feed or just for comfort? I always find things are so much harder and I'm much more likely to feel overwhelmed and even depressed if I'm not getting to relax at night time. When DS2 was about 5-7 months I had a bit of a meltdown myself and ended up on anti depressants and in counselling (which was actually very very good and really helped). Is this something your DH would consider?
How do you feel in yourself? Perhaps a trip to the GP to say how overwhelmed you are feeling and see if there's anything they suggest would help. I'm not saying you're depressed but a lot of what you've written I know I felt when I was very very down.
Bottom line is that it is extremely hard work having any young child but more than one, coupled with sleep deprivation is a killer. I was a mess for at least the first year after DS2. To be honest I didn't cope well with DS1 either as a baby. I find it all a bit of a grind and all a bit too much and you get so little back from them. It's just hard work. It does get better, I promise.