An inter-turbine casing for a turbofan is disclosed. The casing includes an outer ring, an inner ring, and an intermediate ring between the inner ring and the outer ring. The inner and intermediate rings have respective openings for the passage of cooling air. The casing includes at least one sealing device, arranged between the outer ring and the intermediate ring, with a base, provided with at least one orifice for the passage of cooling air, and a peripheral skirt which is able to be compressed and expanded elastically. The base bears against the outer ring and the peripheral skirt bears against the intermediate ring.