It depends how much do you want to change your current project.
In case you don't mind doing complete app revamp think about using Phonegap with jQuery Mobile + Backbone.js or Phonegap with Kendo UI. You already stated that jQuery is used for content loading so jump to jQuery Mobile is not going to be that problematic.
You can still use MVC doctrine with backbone.js and jQuery Mobile will handle page handling/transitions/UI. Only problem with this solution is possible performance issues in case you create too complex app. But this will happen to you no matter are you creating everything from the scratch or because you are using UI frameworks.
If you are willing to give it a try take a look at my other answers on related questions:
- Frameworks and little something about them: https://stackoverflow.com/a/14166593/1848600
- Phonegap + jQuery Mobile tutorials: https://stackoverflow.com/a/14375842/1848600
While Phonegap + jQuery Mobile is far from perfect combination it is still one of the best there is and it will save you a lot of time.
EDIT :
As you are using jQuery Mobile you can have a persistent header and footer if you use:
...data-position="fixed" data-id="footer"...
in both of them.
Here's my "how to" article on this question: https://stackoverflow.com/a/14417307/1848600
And here's a working example: http://jsfiddle.net/Gajotres/Beq4H/