The invention relates to an assembly comprising a resilient, porous base spring layer (14) intended to be positioned facing a surface (12), in particular a motor vehicle surface, and an airtight intermediate insulation layer (16) disposed on the base spring layer (14). The sealed intermediate layer (16) has a mass per unit area of less than 500 g/m2. Thesoundproofing assembly (10) comprises a porous stiffening layer (18) placed in contact with the sealed intermediate layer (16). The porous stiffening layer (18) has a thickness of less than the thickness of the base spring layer (14) and a flexural rigidity (B), at a unit width, greater than 0.01 N.m.