Can't find anything that gives the interior (or exterior) dimensions of the LCF cargo bay, but the 787 fuselage is just shy of 19 ft. in diameter - given clearance and the GSE that the fuselage sits on I'd say at least 20 ft. of internal clearance. Wings as shipped are right at 100 ft. long, so that should ballpark it...

LCF video
 

The video link below shows some footage (interviews with Boeing managers), and might provide some perspective...


As for interior volume, carrying wing and fuselage sections of the 787, there is a scant few inches on the top and sides when the loading system puts the cargo in the belly of the beast.

Another great video (excuse the drama provided by the very enthusiastic BBC reporter!!)...but factually, very correct.

BBC News - The 'pregnant plane' that can give birth to a new 787

From the WBM:

Max fuselage width 23'8"
Main deck floor 126'10" long
Main deck usable cargo volume 65,000 cu ft.

Swingtail door opening:
270" max width
199.8" wide at floor
274" high