OK here goes, I'm a man and have seen a good bit of life so here is my point bearing in mind I have older children who have left home and now have a 9 and 2yr old. When you are starting off it is very hard, there are more and more pressures on people now with both working plus child care costs, it just seems a never ending hamster wheel of work getting paid, paying out all the money to survive and round again, BUT hopefully it will improve over the years.
The key thing is communication, you need to talk to each other, maybe take it in turns to do different jobs, he deals with the kids one night and you cook. I have now retired and I am at home while my wife works, she is 10yrs younger so it will be a good while before she retires. I do everything around the home, well should be doing, but the housework drives me nuts, I am trying to get my head around that, cooking, looking after the children, playing and educating them is great fun, I love putting them to bed, we have a routine and stick to it, they seem to like that. Unfortunately it seems housework including the washing ironing and cleaning is something that will never go away, it is repetitive, I have taken it for granted over the years, pants and socks in my drawers, shirts washed and ironed, I just thought it was normal for it to appear, well I have had a great big shock, so don't think you are the only one!
You are working as well, so that makes me even more guilty, all I can say is both talk, swap roles as each will then appreciate the other, with regards to lights get energy saving ones, electricity bills are not cheap, he is probably just trying to save money, respect him for that as everyone will benefit. Perhaps if he is the saving type work out what you can cut down on to pay for the child care on the days you are off, that way you can get the jobs done.
Good luck, remember there are always people a lot worse off, I have realised that being one here, I should be grateful, not a moaning cow!