A soundproofing assembly includes stacked layers in the form of a first set of layers (36) having good resistance to the passage of air, and a second set of layers (24) with mass-spring function including a layer (28) having a heavy viscoelastic mass and a spring type layer (26); the first set of layers includes a layer (36) of a foam with open cells of high porosity, high tortuosity and good resistance to the passage of air, the layer (36) having, owing to its high tortuosity, excellent sonic absorption properties at medium and high frequencies. The invention is useful for soundproofing motor car passenger compartments.