Years ago, DH and I were fighting about this and he was truely convinced that he had the lion's share of the chores. We got out the handy dandy legal pad and each listed all of the things we did or should be doing. We all know who had the longer list, correct?
Once you have your list in yellow and black, you can start breaking it down by how often, etc. I have to question though, if he is working out of the home and you are home with the kids, how reasonable is it to expect him to do more when you admit you aren't even getting the dishes and the laundry done?
I have four kids, so I do understand, but picking up the dog poop on a daily basis would only take a minute. It's when you let things build up that they become a problem. I found by using Flylady's routines, I do just a few minutes of all of my tasks on a daily basis and nothing builds up.
So, prioritize items and those neither of you really want to do can be hired out. Some neighbor kid would probably like to make a few bucks a week doing the yardwork and the poop clean-up.