Rotate camera with mouse input depending on base rotation of player (3D)

Well... I struggle for quite a long time now with this. To put it simply, i'd like to obtain the same behavior as the FreeLookCam script contained in the Standard Assets of Unity, but whatever the rotation of the character is. Basically, i'd like the camera to rotate around the up vector of the player depending on mouse "x" input.

That can be done quite simply by making the camera a child of the character, but I don't want the rotation of the camera to be affected by the right and forward axis of the player.

I'd like to have something like that :

In any and every case in the 3D world. I sure hope to find someone that is a better mathematician than me. :P