Is sustained inverted flight possible with any of today's commercial jet aircraft?
Theoretically, it is possible to fly an aircraft upside down. Good examples are the barrel roll done by Alvin "Tex" Johnson in Dash-80 (the predecessor of Boeing 707) and the actions of Pilot Flying James Tucker during the hijacking of Federal Express 705. However, the question is whether the maneuver can be sustained for and reasonable periods of time. 

In this matter, the statement of Boeing (manufacturer of MD-80 after merger with McDonnell Douglas) is instructive:


  The MD-80 cannot sustain inverted flight,...The MD-80, as with all commercial airliners, was designed to fly upright. Commercial airliners are only tested and certified for upright flight.


The pilots of Alaska Airlines Flight 261, a MD-83, tried to fly their aircraft upside down for recovery, but were unsuccessful.