Aerodynamics of lift
I am not sure if I got your question completely. 
As I am not entirely sure what you mean by leaving out Bernoulli.

Let's start with the lift issue:
Lift is created when the pressure (-forces) on the upper wing surface (suction side) and the pressure (-forces) on the lower surface do not cancel each other out. Usually this means that there is a net-force pointing upward (in level flight). Lift is therefore not directly connected to the ambient pressure. Does this answer the lift part of your question?
Image taken from wikipedia


Now let's focus on the bulged out surfaces:
I would guess there are at least two effects:


As you can see from the picture above the pressure is lower (than ambience) on
pressure and suction side (but since the pressure on the suction
side is lower than on on the pressure side, there is a net-force
(lift)).
Depending on the aircraft, it could be that the high-pressure in the stagnation point of the wing or aircraft pressurises the wing and cabin which would increase the effect from above. A bit like the canopy of a paraglider.