I'm sorry the argument ended on a bad note. Kids, work stress and tiredness really don't put anyone in a good position for rational discussions. I believe the under 5 years were the hardest of my life!
You mentioned that it is not an option for you to leave the house as he did. Do you mean because of your own principles, values, or it's literally not an option?
Helplessness and lack of freedom, not having options is a horrible feeling. And it's very hard to not start to stack up in your mind how much you've done versus how much he has. Especially as I'm certain you are doing most of the housework. I hated even writing that because in 2017 a part of me wants to believe this can't be true and I shouldn't just assume this.
Him walking out is bound to accentuate that sense of lack of freedom, his liberty and your lack of. If he's out you can't be!
If it's a one off then just let it go, this time in your life is tough enough without turning on each other. However if it kept happening then you'd need to address it.
Get some help in the areas that you aren't enjoying from somewhere other than him if you can, cleaners, child minder, family, friends?
Do you have girlfriends or a community around you, now is a good time to establish some networks, because sometimes what we need doesn't have to come from the home.
I used to imagine I was a single mother and it changed my mindset completely, as in when I stopped thinking about fair share and instead asked myself how I could manage by myself to get rest, take time out for fun/work/study, and be a mother, without my partners help it was easier, less stressful. And any help I did get was a bonus, and actually a lot more than I'd credited him for.
If this was a work project we would agree roles, responsibilities and availability. You say he's normally good at pitching in. Are there some jobs you prefer, it might help if you divvy them up when you are both in a good mood. In our house I always cook but my partner always does the kitchen tidy up. But sometimes this overlaps and that is ok.
I realised I didn't have to make another person do what I wanted to get what I needed for my sanity. Pick your battles and take what you need. You have options if you give them to yourself :)