He is manipulating and exploiting you.
Your DC don’t have a functioning father - he is both emotionally absent and emotionally destructive to them.
They only have one parent and that parent is drained, distracted and preoccupied an emotionally manipulative and abusive partner. Whilst your finite energy, headspace, time and emotion is drained by this emotional leech you have nothing left to attune and attend to you DC. They are missing out here by having two emotionally distracted parents, one threatening and brooding and the other exhausted at the end of her tether.
This will leave them anxious and stressed and they will develop their own behaviour issues and likely chronic MH issues in their teenage years.
This is not an appropriate environment to raise children.
OP, It is clear you will not leave for your own sake. So read this and think of your DC.
If you think it''s too far fetched, it isn't. It happened to me and my DC.
My Ex was abusive. He had severe depression as well, although had a job. He used his depresssion to verbally, emotionally, financially and sexually abuse me. He coerced me into sex acts I didn't want or like.
And remember, coercing someone into sex is illegal.
He was abusive to the DC, although not sexually. And his misogyny showed, as he was more abusive to our DD than DS.
I left after 30 years with teen DC. I was broken.
Both DC have MH issues as a result of the abuse. Depression and anxiety, but both are recovering well, it's over 3 years since we left.
And yes, my ex "attempted" suicide a few times. Nothing serious, turned out they were attempts to reel me back in. I didn't go to him, I called the police on 101 and asked for a welfare check. I realised that if it were genuine, he'd get help. Or, if it was manipulation, the police would have a word. The "attempts" stopped very quickly. 
On the first anniversary of us leaving, he pulled a big stunt and involved our DD in that. I'll never forgive him for that. But I got black and white evidence he was lying about taking an overdose. I kept this evidence to use if he began to try and hassle us again, but in the end I never needed it.
He died late last year from an aneurysm, kids inherit everything.
@BillywigStings, I've read all your posts, and I think you need to take those rose tinted specs off.
This is NOT a nice man. Not the "sweetest, kindest human". Nice, decent men don't coerce their wives into sex, nor do they blame the lack of sex for their "suicidal" thoughts. And that's before we even get into the other behaviour or the refusal to get help.
You need to leave, for your DC and yourself. Sooner, not later.
If you stay, this is your life forever. And it'll get worse, not better.