There are some handy Parallax scrolling JS libs out there they might help quite a bit, take a look:
Scrolling Effect:
http://markdalgleish.com/projects/stellar.js/
Stellar is helpful and easy, it can be as simple as adding data-stellar-ratio=""
to a element, but it can be adjusted with jQuery, it is writen in jQuery, so jQuery will be needed in order to user it.
Gyroscope / Mouse movement Effect:
http://wagerfield.github.io/parallax/
Parallax.js is handy as well, and also very cool, although this isn't a Parallax scrolling like you mentioned, I think you would still like it. Parallax is written in jQuery and JavaScript, so jQuery is not needed.