You shouldn't try to think of an aircraft flying due to either Bernoulli or N3. Basically, there are two fundamental laws of physics that always need to be obeyed. The first one is conservation of energy and Bernoulli's equation is just another way of expressing this fundamental law. The second law is conservation of momentum, which can be written in the form of Newtons third law. As e.g. ARINC already pointed out both of them must hold at once and you can't just say "it's flying because of Bernoulli" or "it's flying because of N3".
Moreover, Bernoulli's equation is often employed using a wrong model, i.e. that two molecules from the air stream split at the leading edge will meet again at the end of the wing which, if you don't have a flat plate, would require the air above the wing to move faster, thus producing a lower static pressure above it, resulting in lift. This isn't true and, if you do a rough estimate, leads to the result that the lift would be very small (I read somewhere that a Cessna would only take off at about 400 mph's if this model would be true!). But, unfortunately, it's still taught quite often and you will find in lots of text books on this subject.
Actually there are two contributions producing the lift, coming from both the sides of the wing. Already when you have a flat wing with an certain AoA you get lift from the bottom of the wing because the molecules of the air bounce against it and get deflected downwards, resulting, due to N3, in a corresponding upward force on the wing (plus, of course, some drag which you need to compensate using the engine).
On the upper side of the wing things are a bit less easy to visualize, here you have what's often called the Caonda effect. Just imagine again that you have a flat wing with a certain AoA. If the air would move completely straight (i.e. horizontally) above the wing it would pull away some of the molecules behind the leading edge of the wing (on the lee side) due to friction. That would produce a lower pressure where these molecules now are missing, pulling the following air mass coming over the edge of the wind downwards. As a net result the air going over the top of the wing also gets accelerated downwards, adding further lift, again due to N3. Actually, this second contribution seems to produce the major part of the lift.
There's a very simple experiment demonstrating the Coanda effect quite nicely. All you need is a spoon and a faucet. Open it so you get a constant non-turbulent flow and then move the backside of the spoon slowly from the side into the water stream. You will notice that the water won't move straight down anymore when the spoon comes into contact with the water but gets deflected in the direction of the spoon and you also will feel quite a strong force on the spoon, trying to push it further into the water stream. Now turn everything by 90 degree, replace the water by air and the spoon by the wing and you have what happens at the upper side of the airfoil.
If you now want not only a qualitatve picture but want to get into the nitty-grity details of the exact forces on the different parts of the wing of a certain shape then, as Ghengis the Engineer already pointed out, you need the Navier-Stokes equation to get the (more or less) complete picture. But that's left as an exercise to the reader;-)
Just for those curious about conservation of momentum: even in level flight air must be accelerated downwards in order to have enough upward force on the wing to counter gravity. But that means that a downward momentum is created (the air deflected down) while the aircraft stays at the same height, thus no change in its momentum. Naturally one would ask "Where's the upward momentum to satisfy conservation of momentum?" The answer may sound funny: the upward momentum goes to the earth below. While it tries to pull down the aircraft at the same time it gets pulled up to the aircraft with exactly the same force, (it just doesn't move visibly because it has such a higher mass), resulting in a momentum exactly opposite to the one of the air accelerated downwards.