He walks around with one, but then the second "pops" out from under his chin basically. When the second one pops up past the collar (complete with a "pop" noise), it's one head on top of another and you see both. Then he gets mad and shoves the second back down so it disappears under his turtleneck collar again.
It's a big silly how it's done, but the movie's still good overall.
-m