The B O T T O M of ceiling joists is where sheetrock is mounted -- usually.
Here and there, you'll see open joists (at the bottom) -- for 'the look', in which case, the ceiling is mounted 'high and low' between the joist beams and their bellies.
'Unfinished joists' suggests F L O O R joists -- and the unfinished space would face a bottom cavity.
Unfinished ceiling joists -- that's a new one for me.
=======
As for Harold's notions: that's the way I've always run Romex and MC in wood structures.
Another location, which is what the OP might have had in mind, would be PURLINS.
http://en.wikipedia.org/wiki/PurlinThe underbelly of purlins are used for Romex and MC runs all the time -- consistent with the NEC. It is extremely common for such purlins to run bare.
