have you been sat on your arse all day? 
if the house is in that bad a state then clearly something needs to be done! It's not good that your child is embarrassed to have friends round, and if it's that bad that children are falling over stuff then it's a problem, isn't it? It's not nice to live in a mess.
But that is separate from the question of who does it!
I have thought that the fairest way to work things is to think of it as a working week. So, say, he works 10 hours a day outside the house, you do 10 hours a day for your 'working week'. anything that can't be done in that time is done as a 50/50 split.
That's reasonable, right?
Both of you do the same hours. (I don't mean get timesheets or anything just roughly.)
What isn't acceptable is when one party thinks that because they work outside the home, then everything IN the home is the responsibility of the other person. Because then you have a situation where one is doing a 40 hour week and the other is doing more like 90! daytime, evenings, weekends.
But regardless all that, he's not your boss, your commander, your lord and master and if he thinks there's an unfair split of tasks, then he approaches it as your equal and he doesn't bloody throw his weight about.
Someone approaching me like that would get zero cooperation from me! and I wouldn't blame you for thinking well fuck you very much, mate