Any type of flat surface will fly if the proper angle of attack at a sufficient airspeed. That is, it will fly but not necesarily very well. With a semi symetrical wing profile, the AoA for inverted flight will be significantly different than for right side up flight and that will also change the performance and so on. An airliner will most likely not be able to fly inverted with this theory in mind because of the extra thrust required. It may pass the inverted state though in a roll for example (reference to the B707 famous test flight), but this is not flying inverted in the same sense as it is during a transition in a roll with positive G's.
Aircraft that are supposed to fly inverted tend to have a more symetrical type of airfoil and this will make the difference between inverted flight and right side up less apparant in regards to aerodynamics.
Hope this answers your question.
/LnS