Here's my thoughts - spending that much time on the 'job-search' is really counter-productive. He should devote a few hours to it every day, but then move on to other things. He needs his mind fresh and being stuck in job-search mode is demoralizing and saps one's creativity.
I was unemployed for the six months prior to our first child being born and then almost a full year afterwards. I woke up, exercised, did job searching (emails, cover letters, LinkedIn..etc) until around noon daily. Then I helped around the house, went for walks, read books, wrote, volunteered with groups that I was passionate about (international adoption policy) and made all of the meals. I liked being able to clean our apt, because it put me in a different head-space. If I thought I had a productive day, I 'rewarded' myself by watching some Netflix.
I was again unemployed for most of my wife's pregnancy for the 2nd child. I did most of the same, but this time I took care of our daughter (then 2) as much as I could, since my wife was both working and in school.
I'm sorry you have to go through this. It's definitely not fair to you and I think he's being completely unreasonable. As the other commenter said, therapy might be useful here.