A compressor housing resistant to a titanium fire (burning titanium). A mixed housing is constructed, in which a structure holding stator blades includes a single-cast part made from titanium or titanium alloy, and at least one element forming a shield made from refractory alloy(s), and which is incombustible in presence of burning titanium, where each shield is secured to the single-cast part by fasteners. The fasteners are positioned with each shield so as to define jointly an inner wall demarcating an outer contour of the compressor airstream.