Hey there! I'm considering a double major in Public Health and English so I'm in a very similar situation...it's definitely doable, but you won't be able to take as many "random" classes just for fun.
A plus, however, is that you don't have to worry about your IS distribution requirements. Since the Public Health Studies major is interdisciplinary within itself, you don't need distribution requirements. If you choose to double major, you only have to fulfill the distribution requirements for one major, and you already do that with Public Health!
I'm also looking into the 5 year program, but I am not sure how competitive it is. Here's some more information on the program: http://www.jhsph.edu/bin/y/l/BAMHS11.10.pdf