I was a childless woman for a very very long time - much longer than most I was single and 41 when I had DS so I consider myself to have the backs of childless women on bitchy threads.
It is relevant that these women are childless - you can't possibly grasp the despair of sleep deprivation until you've experienced it. MOst of us (when childless) have the empathy to understand that and just make soothing noises.
To be fair they were probably just saying what your DH wanted to hear or maybe it is genuinely what they beleive - either way its not a big problem except that its what your DH believes - which is a problem.
I'm single I managed DS completely on my own. No lie-ins, nights off, no-one to make me a cup of tea or a meal. It's hard sometimes. I thought the point of having a partner is that life is easier together than separately? 
I guess he thinks that the money he provides is everything (of course its something as I would have liked that too!) but its not everything.
You should agree what hours you both "work" make sure its even (so if baby naps during the day then that isn't work time if you use it to sleep or relax but is if you use it to do housework cook etc) then divide all other time evenly between you.
Its a bit clinical but if he's going to be an arse about it then you'll have to be too. And I didnt have to clean up after an extra person or cook for him etc etc - why would you do this? WHY?
He's an adult if he were single he would be working and cleaning and cooking for himself - did he get married or buy a slave?!