I've been struggling with this too and spent the morning hacking on JQM to try to fix it. I got close, but kept running into little problems.
Basically, I think the query format is technically supposed to be:
I got this pretty close to working but I ended up with either the history/back button not working properly, or losing the ajax-ness, which defeats the purpose.
Basically, JQM isn't expecting a param in the string, so it just strips it out. I fixed that, got it to load the page and show it, but what I couldn't quite get working is to get JQM to leave the URL alone. In the example above, the URL ends up stripped of the search query.
I really hope we're missing something here, because this is pretty much a show stopper if I can't build applications that pass state between pages in a clean way.
My hope is that someone who knows the code better knows of a simpler way to make this behave properly - the main problems seem to occur in loadPage and changePage.