Chris is pretty close on this one. However, if you notice, at air shows for example, when a small aerobatic aircraft is flying upside down, the nose of the aircraft is fairly high on the horizon and the aircraft creates an arc from the start of the manuever to the end. That is, it's flight path is curved, especially descending towards the end. The reason is that the wing of the rather underpowered aircraft is more symmetrical than a standard small aircraft wing that gonzo00 described. It can fly almost equally as well upside down, but not quite as good as right side up (due to a lot of drag caused by being upside down). Therefore, as the continued upside down flight continues, the aircraft, to maintain the minimum airpseed required for inverted flight, trades off some altitude witnessed by the arc and descending flight. (Normal flight, by the way, is also dependent on Newtonian downward thrust of the air as it moves aft off the wing).
This doesn't apply to high-powered jet fighter aircraft. They have so much excess power that, in effect, their small very thin wings are more like stabliizers than actual lift providing surfaces (although they do that as well).
There are many older aircraft that are used in airshows that weren't really intended for inverted flight. Their fuel and oil systems weren't designed for it, but more importantly, the fairly thick wings can only provide a small amount of lift inverted if the nose of the aircraft is abnormally high in relation to the horizon. This has some analogy to the skipping of a rock in a pond. It keeps skipping until enough of its speed is bled off and then it sinks. The aircraft would too, in an inverted stall if allowed to proceed very far inverted....
Want to know how an airplane flies straight up?