Controllers (joystick) binding not detected correctly

Context
I'm trying to setup my controller to work correctly with PCSX2 (version 1.4.0).

Material
I installed PCSX2 and got a game working correctly, but my problem is with the controllers.

I have a controller like a PS3 controller (brand Under Control), so with the buttons triangle, circle, cross, square, with a right joystick, a left joystick, a D-Pad, and L/R 1/2/3.
Here's a photo:
Attachment 54634

I have a computer with Windows 10 x64, Intel(R) Core(TM) i5-7600K CPU @ 3.80GHz 3.79GHz and 16Go RAM.

Problem

When trying to bind my GamePad to LilyPad, LilyPad doesn't make a difference between when I action my left joystick and my D-Pad (I can't have D-Pad AND Left analog stick working at the same time, because when I set correctly one, the other is overriden with Axe X +/- and Axe Y +/- PC control). The same happen with the shape controls (square/triangle/circle/cross) and the right analog Stick (respectively Left/Up/Right/Down).

See below for a visual description of the corresponding areas.
Attachment 54632

Question
How do I setup all my buttons without unbinding the others, in order to have all buttons working at the same time?

Thanks for your response and time.