I also am a stay at home mom with 3 kiddos...
Hubby and I have had our own discussions (most of them ending with me deciding its not worth the fight when he pulls out the " I work a 60 hour a week job and drive 2 hrs a day... etc" card. (I don't fight stupid battles... Noone wins and it causes issues)
BUT...
I am blessed with a hubby that does help out.
He helps set the table and occupy the kids while I am cooking. He also helps clear off the table and he puts the food away.
We have a 7 yr old that earns her allowance by setting the table and clearing it off... He supervises.
Other wise, I am incharge of all the laundry and ironing, cleaning, cooking, daughters homework, phone answering and appointment making, dog walking thru the week, kid care and picking up thru the week, grocery shopping, and car pool for DD school, taking cars to get maintenence on them, cat care, fish care,vacuuming, snow shoveling thru out the week, and all other odd and end things like putting furniture together and unclogging drains.
He is a blessing to me because he does help with the table, putting the food away, he puts the kids to bed, walks the dog on weekends, does weekly maintenance on our vehicles to make sure they have enough fluids in them, helps pick up after the kids on weekends, changes diapers (even the poopy ones) Builds very nice furniture if we need it (fish tank stand, and bed frame), shovels the paths thru the snow on weekends, changes the cat litter box, and the biggest of them all is occupies the kids when mommy just needs 2 seconds of no slobbering on her.
If you look at the lists mine is the big stuff, his is little things. But I also don't have the pressures he has while he's at work or the commute. I don't HAVE to get up at 4:30 am to get to work on time, and arrive home just at dinnertime. And honestly, I would probibly just get upset at him for not doing things "right" aka the way I would.
Hubby realizes that mommy has different stresses on her than he does and sees when I am getting frazzled.
I look at it as one of the things most stay at home moms have to deal with. But don't worry, your oldest child is getting old enough to help out a bit. My 7 and 4 yr olds LOVE helping mommy in the kitchen and our 7 yr old is incharge of putting HER clothes away.
You have just had a baby so your work load is heavier with an infant than it will be as the child ages. Take one day at a time and orginization is a must! Practice makes perfect and unless your hubby (or you) are OCD you can let things slip a bit. I do not dust more than every few months. (hubby will do it before I will)
Sit down with hubby and tell let him know that you need some assistance since the baby has come. (You can even use the hormone card) ASK him specific things to do. Then let him do it his way. Communication is the key.