NACELLE INLET STRUCTURE WITH FOAM CORE

An assembly (54) for an aircraft propulsion system (20) includes a nacelle inlet structure (34) extending axially along and circumferentially about an axis. The nacelle inlet structure (34) includes an inlet lip skin (58), an inner barrel (60), an outer barrel (62), a foam core (68) and an acoustic structure (66). The inlet lip skin (58) forms a leading edge (70) of the nacelle inlet structure (34). The inner barrel (60) projects axially aft from the inlet lip skin (58). The inner barrel (60) forms a perforated face skin (110) of the acoustic structure (66). The outer barrel (62) projects axially aft from the inlet lip skin (58). The outer barrel (62) is radially outboard of the inner barrel (60). The foam core (68) is radially between the inner barrel (60) and the outer barrel (62). The foam core (68) axially overlaps the perforated face skin (110) and projects axially to the inlet lip skin (58).