The technical term is “jerga” (pronouced hair-ga").
Yup, I’ve got one too – haven’t worn it in years, but I still love it.
The thread title made me think of the Cake song Short Skirt / Long Jacket.
I’m agreeing with Bear_Nenno here and calling it a poncho.
Interestingly, I found this photo doing a Google Images search on “jerga.”
Maybe that’s the Spanish name for them. I’ve only heard “bajas.”