An assembly is provided for an aircraft propulsion system. This assembly includes a nacelle inlet structure, a thrust reverser and a fan cowl. The thrust reverser includes a forward portion and a translating sleeve. The fan cowl is axially between the nacelle inlet structure and the translating sleeve. The fan cowl axially covers the forward portion of the thrust reverser. The fan cowl is axially structurally tied to the nacelle inlet structure. The fan cowl is radially and circumferentially structurally tied to the forward portion of the thrust reverser.