The hemispherical transmittance of free standing films (1-20 microns thick) of polycrystalline diamond grown with a filament assisted chemical vapor deposition (FACVD) system and an oxygen-acetylene torch has been measured. Measurements were performed in the infrared (2-16 microns) with a Fourier Transform Infrared Spectrophotometer (FTIR) equipped with a diffuse gold integrating sphere and in the ultraviolet, visible and near infrared (0.20 - 2.5 microns) by a dispersive spectrophotometer used with an integrating sphere attachment. For FACVD films of approximately 1 micron thickness grown with a small amount of oxygen in the chamber, strong interference effects are observed in both spectral regions, and the total transmittance was above 60% in the visible and MR. The best films grown in the oxygen-acetylene flame show a sharp band edge at 220-222 nm, and a transmittance at long wavelengths (> 16 microns) which approaches 70%, for film thicknesses of 10-20 microns. These features are comparable to type IIA natural diamond. The optical transparency of the flame grown films is sufficient to read newsprint when held next to the text, however the large grain size (2-5 microns) and rough surfaces introduce sufficient scatter to blur the image of the text as the film and text are separated.