YOu sound like a very nice unselfish person and your dh is taking advantage of that.
My dh does absolutely nothign around the house (and creates a lot of mess) so I understand your frustration, but he works very long hours and I work only a few (expat situation) so I'm not in a position to protest. Plus, given his work load and travel schedule, he is a very involved father and enjoys shopping for food and cooking etc when he is here. He also happily runs lots of errands although I am sure this is to avoid housework 
Think Hermitcrabs suggestions are very clever and subtle and much better than mine, but fwiw ....
In your position, if he still doesn't get it, I think I would organise a proper meeting with your dh outside the house. (This should have happen 4 yrs ago
but better late than never!) Plan childcare and organise it like you would a work meeting. Write out your objectives and what you want to achieve by the end of it. Also, sort dates for implementation and set another meeting (perhaps two or three months on?) for a review of how it is working. That way he gets the message that you are serious.
Tell him you feel totally and utterly unappreciated in every way. That you are unhappy and that things have to change. Be unapologetic and unequivocal. This situation is not your fault. He needs to receive this message loud and clear.
There's no need to nag. Having written down all the tasks you do (everything!) over the previous fortnight or month, just present him with a list and then agree a 60/40 split or whatever you would be happy with.
Incude your dc in the chore list too (you don't want them to grow up like him!)
Be strong over the implementation period. Do not bail him out ever! (It would help, as previously suggested, if some of the tasks he does impact mostly on him if left undone ie his work shirts, his food etc.) Just stick to your tasks resolutely and ignore the rest. If things are left undone, refer him to the list. Make him feel accountable.
NO need to reveal this at the outset, but I think you need to decide on a consequence at the end of two or three months, if he doesn't comply. (Plan time away to think about things, book yourself a holiday, a trial period living on your own. It depends on how strongly you feel about all of this and how far you are prepared to go to achieve equality in the chore dept.)
Once the housework is sorted, you then have a clear space in which to work on the rest of your relationship.
Sorry for huge post (I the flu, so high temp must be making me ramble) All of the above is of course much easier to write down than to implement! Rlis not that easy! I have a sister who has had the same issues throughout her married life and only now, upon retirement, is she starting to address some of them. She wishes she had done so much earlier ... .
Good luck 