So many emotions as I read this. Wonder at the birth of the puppies and sympathy for your own contractions.
But... re. you not telling your husband it's your birthday - that's sorta passive aggressive, I think.
If celebrating your birthday matters to you, and it should, then you need to tell him that. At the same time, acknowledge that not everyone is good at remembering dates.
My ex entered important dates like family birthdays into his calendar. He wouldn't have remembered otherwise, but thanks to his organizational skills, he never missed a birthday.
I'm totally absent-minded about birthdays, but I usually remember within a couple of weeks of the actual date, plus or minus. My loved ones get this. They know I WILL remember, just not the exact date - and this now adds to their surprise.
This is my personality, but for loved ones that really care about me remembering the date - I now take a page out of my ex's book and set a calendar reminder for myself.
Not sure what strategy will work for your husband, but it's better to talk this through with him and find a solution rather than continue to be hurt by his obvious cluelessness. Obviously though he's a good guy, aside from that.