mixing JQuery Mobile with JQuery UI widgets... don't ?

mixing JQuery Mobile with JQuery UI widgets... don't ?

Forgive me if this seems like a silly idea to begin with, but to "tide me over" while certain JQuery Mobile widgets do not exist yet (calendar, tabs etc.) I thought I'd just load up JQuery UI and bring those widgets in from there.
It was not pretty.

Are the two not supposed to co-exist ? Wouldn't it be nice to leverage JQ UI widgets in JQ M applications ? 
Or is their CSS / js base too different to make that practical ?
Or - should it work and I just screwed up in which case I will try again :)