Haven't read the whole thread but, no, in this household things are not truly equal. They are more equal than they were but most of the nitty gritty of parenting falls to me and always has done.
Dh has never taken them to buy shoes, he has never bought any of their clothes, party invitations (buying presents and the like) fall to me - as does buying birthday and Christmas presents for our children (and his family, but let's not get me started on that, eh?) If I went away for any length of time I would have to leave fairly detailed instructions - the reams of instructions attached by magnets to the front of the fridge when I went into hospital to have ds2 would bear testament to that. He rarely takes them to, or picks them up from, school - in fact, I think I'd have to remind him what time they finish.
But, the crucial thing is I don't mind (mostly ). He works very long hours in a demanding job; I work part-time from home. The arrangement suits us. And when he is here he is hands on, he makes packed lunches in the morning, he does bath-time, he never shirked from changing nappies - he's as involved as he can be given the reduced time he's actually with the boys.
It's not all perfect - he has a tendency to let them play on the X-Box/watch TV for rather longer than I do - while he surfs the net or reads the newspaper...and he also tends to over-react to normal, minor bad behaviour, whereas I tend to let the small stuff go so as not to spend the whole day shouting.
That all sounds kind of smugsville - it's taken us almost 10 years to get to a state of equilibrium, if not equality. He did nothing with ds1 - I wouldn't let him. I had severe PND, which was a major factor - I practically left him and moved in with my parents fro the first 6 months of ds1's life, so he never had chance to bond with him . I wouldn't let him take any of the responsibility for parenting and as a result he had no confidence in his ability as a father and abdicated everything to me. He never took ds1 out on his own, never got up to him in the night - when he got older he didn't read bedtime stories, didn't give him a bath. If I was going to bed and he wasn't - I would take the monitor with me and get up if ds1 cried - that's unbelievable to me now, but it's what we did. Thinking about it, I can hardly believe how much he - we - changed when ds2 came along: the division is much more equal and, as a result, he had a much closer relationship with ds2 as a baby/toddler than he did with ds1.
So I went from smugsville to a ramble..ah well..