How much should I expect my husband to help out with household chores?

I am married with a two year old and a dog. I work part-time. Lately, I've been really depressed on my days off and look forward to going to work. It seems that the only thing waiting for me at home is a mess to clean up. I have asked my husband to help me by just picking up after himself. I would say that I am not satisfied with his efforts. Occasionally he will either start the dishwasher or unload it, but I can never count on it. He doesn't work a regular 9 to 5 job, so he often time has a lot of time to himself at home. All by himself...our daughter goes to daycare when I'm working regardless if he is at home. He spends this time on whatever hobby seems to captivate his interest at the time. For example, Today I went to work. My daughter went to daycare and my husband "played" all day and worked on his 'project" in the garage. I fed our daughter, changed her diaper several times, read her a story, gave her a bath etc all while my husband worked on his "project" in the garage. Today he actually put the garbage container in the backyard after the trash pick-up. This is amazing because this happens about once every two months that he decides to do this on his own initiative. The clean dishes were still in the dishwasher though. I do about 15 loads of laundry per week. I pick up all the toys strewn about and the paper that the dog may decide to shred. I vacuum several times per week (dog hair). He leaves cups and bowls in the bedroom very frequently. It seems he will only do something if it affects his immediate comfort...like put sheets on the bed b/c he's ready to go to sleep and I haven't got them back on yet. I really don't nag him...or at least I monitor myself and pretty much know that I have expressed to him a desire for him to help out some...and with that I hope that somehow he can somehow muster up some internal motivation to HELP ME! I don't want to nag. This is so depressing and gets me really down to constantly be cleaning up after everyone with nothing to look forward to except the next mess that will occur in the very near future. Even though my husband does a great job with the yard work, should he contribute more around the house with daily chores?