That was my first Batman figure, too.
I also had Robin (with karate-chop action) and the Batmobile. I remeber the Penguin was too fat to fit into it, and the Joker could fit, but you had to take the tails off of his coat first.
Those were great toys.
Yep I had just about everyone and everything to do with that toyline including quite a few doubles. The toys were just so much fun and honestly there has not been a toyline as good since which is a real shame. I am an avid collector of super powers merch and hopefully soon can continue my collecting. A lot of really great memories tied to that toyline (and many others from the 80's)