How about this CSS only solution:
https://jsfiddle.net/Volker_E/jwGBy/24/
body gets position: fixed; and every other element you wish an overflow: scroll;.
Works on mobile Chrome (WebKit)/Firefox 19/Opera 12.
You’ll also see my various attempts towards a jQuery solution. But as soon as you’re binding touchmove/touchstart to document, it hinders scrolling in the child div no matter if unbinded or not.
Disclaimer: Solutions to this problem are in many ways basically not very nice UX-wise! You’ll never know how big the viewport of your visitors exactly is or which font-size they are using (client user-agent style like), therefore it could easily be, that important content is hidden to them in your document.