Dielectric aperiodic Thue-Morse structures up to 128 layers have been fabricated by using porous silicon technology. The photonic band gap properties of Thue-Morse multilayers have been theoretically investigated by means of the transfer matrix method and the integrated density of states. The theoretical approach has been compared and discussed with the reflectivity measurements at variable angles for both the transverse electric and transverse magnetic polarizations of light. The photonic band gap regions, wide 70 nm and 90 nm, included between 0 and 30 degrees , have been observed for the sixth and seventh orders, respectively.