I agree that he may well have the male version of PND.
I also think that both of you need to realise that these really tough baby years are only going to last another 18 months or so. Dd2 will be two and a half-ish by then, and that's about when it all starts to get easier.
Baby years are tough. The two of you though, arguing about who has had two nights out since dd2 was born, and who has had none, are playing a silly tit-for-tat game which needs to stop. I don't mean to sound harsh because I fully understand how it gets to this - I'm pretty sure almost every couple has felt those things, if not said them. In the end, someone is always going to get an easier ride than the other. In my marriage, it was my husband. He ran his own business (a hotel) and made sure he was out of the house 7 days a week from the minute he woke up to after we'd gone to sleep. Breast-feeding was a godsend for him, because it meant he could also ignore the night feeds! At the time, I loathed him, I have to admit.
But things have got better. He's still a lazy arse, but he has his good qualities.
I remember my sister also loathing her dh during the baby/toddler years.
I just feel that if you can get through the next 18 months to 2 years, then you might be home and dry.
Don't compare who's had the most 'time off', or who has it easier - that is the way to ruin. Just seethe inside and if you want to go out, and he's not stopping you, then do so. But don't compare. As they said on another thread, comparison is the thief of joy.