Your game has very good approaches, however, there are a few flaws that bother me quite a bit.
First the good things: music and graphics are well chosen.
Also, the character doesn't seem quite as floaty as it often does in gamejams.
Now for what I would do differently:
The player's collider is annoying. A simple box achieves the same effect and you don't get stuck with your nose.
Furthermore, you always get stuck on the sides of platforms. I would definitely remove that. In Unity you can easily work around this with the "Platform Effector 2D".
Also, the coupling function doesn't seem to work so well. Sometimes the character is swapped back, sometimes not, plus it doesn't seem to have any effect when the other char dies. No idea what you tried there.
All in all, though, I enjoyed your game. Please don't let my feedback drag you down. :D