A composite insulation is included between the skin of an aircraft and interior trim panels. The composite insulation includes multiple layers of micro-perforate material interspersed with layers of semi-rigid material. For a given thickness, the composite insulation provides superior transmission loss over a wide range of frequencies, including low frequencies, compared to conventional homogeneous insulation having the same thickness. Thus, the composite insulation reduces broadband noise within the cabin of an aircraft more effectively compared with a conventional insulation.