Hello Soverign. I think most of your partners behaviour stems out of his depression. Looking at his behaviour it does seem similar to several people I know who suffered depression. Not all of it though, he does sound like he has some growing up to do and responsibilties as a father he needs to step up to.
Real depression can cause a man to loose interest in work and family life. They can feel hopeless, helpless, irritable and intolerant of others, a lack of motivation and little interest in things and various difficulties in the home and family life go hand in hand.
So the truth is if you are suddenly hoping now you're separated that his attitude is going to change as he'd have a reality check, it probably won't. This is IF it is genuine depression and not laziness or selfishness? 
But then again his attitude won't change if it's those instead either
Not being bothered to see the kids or turn up for a meeting about you both is likely to be part and parcel of his whole attitude. He also may have a little more way to go before he hits rock bottom and he may react in a variety of ways whilst he gets there.
The truth is he needs to go to his GP and get some help and counseling. Otherwise he will remain in this rut.
However, hard as it is after 11 years together, you need to look after yourself and the children and try to detach from him at this time.
In an ideal world if he wasn't depressed, all these issues could have been overcome between you with some good counseling from Relate. However in this situation I truly do not think it could be successful because of his general attitude and issues. Please stop tying yourself in knots about him and what has happened as others have said(easier said than done).
I can't help wondering whether something in your past when growing up is also a factor in why you are so quick to blame yourself and feel guilty for this whole situation? As others are completely right this isn't something you should feel guilty about. Fontella speaks such sense and is so right as well.
I know you want a stable father figure for your kids but (as I often say on peoples threads and was also quoted to me when deciding to divorce my cheating husband) it is equally important that your children see their mother being treated with love and respect, both by a partner and by herself.
The message we send to our children when we sell ourselves short by accepting far far less than we should can have a profound impact in how they see themselves as adults and their expectations from relationships.
You do your children no favours by perpetuating this situation. At the least, they will understand that their mother values herself too highly to be treated poorly, and this is a far greater example to set for them.
I had an ex who cheated on me as I said, and towards the end I became so focussed on trying to salvage the relationship, I realised that I stopped asking myself whether I actually wanted to be with him until someone on mumsnet challenged me 
I know it's much harder because of the children, but seriously, if you had to describe the kind of partner and relationship and father to your kids you would like to have in your life - is he any of those qualities?
When the dust has settled and you have some distance on it that you will see the relationship differently. Everything is clearer in retrospect. For when you give up the fear of losing him, you can calmly evaluate - is this what I want?
Keep being honest with yourself, and try not to make decisions based on fear - they are always our worst choices. You WILL be fine without him, afterall you were already doing most of the childcare anyway.
I cannot blame you for putting something on facebook. I can imagine how angry you were. However I think because of who he is though, he may not make the effort you long for him to with the children. Try to detach as I said. Forge a life out for yourself and the DCs, do things together with your children and try to move on with your life whilst he probably hits rock bottom in his. He is no longer your respondisility, only your lovely DCs are x