Best advice I was ever given?
If you find yourself feeling depressed, before relying on labels and medication, first make sure you are not surrounded by assholes.
I am not trying to deny the existence of PND, which is of course a medically confirmed, highly debilitating medical condition. However, in some cases I think women are actually reacting perfectly normally to having completely inadequate support at home, whether that be through lack of family support or twattish DHs.
The fact that your DH sees it as his role to grant or deny you child-free time from a child that is 50% his responsibility, sadly leads me to believe he is being a twat. 
However, if there is much to this than your opening post, and your DH is doing his fair share and is himself knackered, and the truth is that you have a difficult baby and there isn't enough of you and your DH to go round no matter how hard you both try, then that's different. CAn you get help from the GP or Home Start? Or a friend?
Hope you feel better soon.