Porous silicon is a nanostructured material and exhibits efficient photo- and electro-luminescence in the visible range at room temperature, as well as a tunable refractive index determined by its porosity. Porous silicon samples can be obtained by etching a crystalline silicon wafer in a solution of hydrofluoric acid. In this work, we report the fabrication of porous silicon multilayers alternating layers with high and low porosities, which correspondingly produce low and high refractive indices. The free-standing multilayers were formed following three different sequences: periodic, Fibonacci and ThueMorse. These structures were verified by scanning electron microscopy and their infrared transmission spectra were measured by means of Fourier-transform infrared spectroscopy. On the other hand, we calculate the light transmittance of porous silicon multilayers by using the transfer matrix method for all directions of incidence and a wide range of wavelengths. The experimental measurements are compared with theoretical results and a good agreement is observed. In addition, an analysis of infrared absorption peaks due to the molecular vibrations at pore surfaces reveals the presence of hydrogen and oxygen atoms.