IMHO, most could be flown into the inverted position - the prototype 707 was barrell rolled. Holding it inverted would not present too much of a problem either. Although all airliners will not be cleared for inverted flight, the structure should be able to take it.
The problem comes with feeding the engines. Of the big aircraft I have flown, only one has had a system to maintain fuel pressure under negative g - and that was a military jet.