The assembly comprises a base spring layer made with a base of a resilient porous material, and the base spring layer being intended to be placed opposite a surface of the automobile. It comprises a stiffening layer arranged above the base spring layer and having a surface density greater than 250 g/m2 and at least one resilient porous upper layer arranged on the stiffening layer. The stiffening layer is made with a base of a dense porous material having a resistance to air flow strictly greater than 2000 N·m−3·s. The assembly advantageously has an upper resistive layer.