Is it possible to fly a large aircraft inverted?
In the movie Flight (2012), Captain Whittaker (Denzel Washington) does not explain why he deliberately inverted his aircraft, but the obvious inference is: since the horizontal stabilizer has slipped off its jackscrew and become jammed into a descent angle beyond the authority of the elevators to correct, in inverted flight this would push the nose far above the horizon and result in either a climb or a stall.

In this attitude, Whittaker would have been pulling back on the yoke to prevent the stall.  In the movie, this worked.  The aircraft was still not under control, but was no longer diving and overspeeding.  Suddenly rolling the aircraft upright in the last seconds before contact with terrain is the unrealistic part.  A hot fighter jet might accomplish this but the roll rate of a passenger jet is too slow.

The movie's flight emergency is based mostly on the crash of Alaska Airlines flight 261 on January 31, 2000.  In that incident, the pilots experienced a jammed horizontal stabilizer with uncontrollable dive, and inverted their MD-80 to arrest their descent.  Unfortunately in real life neither flying officer was stuffed to the gills with booze and coke: the maneouver failed and the aircraft crashed with no survivors.