Well, yes, but also no.
You care correct that if you took a plane that was flying perfectly straight and level, and inverted it, the lift (from the wings) would now push the plane towards the ground.
BUT, a plane can still pitch down, pushing opposite the wings’ lift, and go down. While inverted, that can help keep the plane from falling.
Another factor is the fact that any plane that can fly for extended periods of time (typically fighter jets) rely more on the direction of their thrust (by angling up while flying) than the shape of their wings to stay airborne.
Thus, while flying upside down, they just need to keep their thrust “pointed somewhat towards the ground”, which will push them back up.
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