This paper reports broadband THz free-space transmission measurements and modeling of indium-tin-oxide (ITO) thin films on p-doped Si substrates. Two such samples having ITO thickness of 50 and 100 nm, and DC sheet conductance 260 and 56 Ω/sq, respectively, were characterized between 0.2 and 1.2 THz using a frequency-domain spectrometer. The 50-nm-film sample displayed very flat transmittance over the 1-THz bandwidth, suggesting it is close to the critical THz sheet conductance that suppresses multi-pass interference in the substrate. An accurate transmission-line-based equivalent circuit is developed to explain the effect, and then used to show that the net reflectivity and absorptivity necessarily oscillate with frequency. This has important implications for the use of thin-film metallic coupling layers on THz components and devices, such as detectors and sources. Consistent with previous reported results, the sheet conductance that best fits the THz transmittance data is roughly 50% higher than the DC values for both samples.