An assembly (1) formed of a wheel comprising a rim (3) equipped with an inflation valve (4), a tire (2) mounted on said rim (3) of said wheel, and a foam insert (5) placed inside the volume defined by the internal wall of the tire (2) and the wheel rim (3). The foam insert (5) is disposed in a first compartment (A) in communication with the atmosphere via a duct (36) and isolated in airtight manner by a flexible membrane (51) from the rest of the space (B) inside the tire casing, which space forms a second compartment (B) in communication with the inflation valve (4, 41) and designed to be inflated to the utilisation pressure of the tire. At least one of the edges of the membrane (52a, 52b) forms an airtight joint with the rim (3) along a circular bearing surface (32a, 32b), separate from the rim seats (31a, 31b) designed to receive the beads (21a, 21) of the tire (2), and situated axially inside the space between each of the seats (31a, 31b) and the sidewall of the foam insert (50a, 50b) positioned opposite said seat.