An aircraft propulsion assembly equipped with a thrust-reversing device which includes at least one lateral aperture, passing through the nacelle of the propulsion assembly, configured to be in an open state or a closed state, at least one inflatable barrier configured to be in a deflated state in which the barrier does not protrude into an annular duct channeling a flow of air and an inflated state in which the barrier, substantially rigid or semi-rigid, is deployed and extends across the annular duct to deflect at least a part of the flow of air toward the lateral aperture, and at least one supply system configured to supply the inflatable barrier with fluid. An aircraft is provided which includes at least one such propulsion assembly.