Using freely propagating terahertz radiation, we have measured the complex dielectric constant of optically thick layered materials from 0.2 THz (6.6 cm−1) to 6 THz (200 cm−1). Transmission measurements of a CdTe–adhesive–Si structure have been successfully fitted to a theoretical model over the measurement range. The accuracy of the theoretical fit shows that the technique of time-domain spectroscopy offers advantages over other spectroscopic methods in the extreme far infrared below 200 cm−1. The signal-to-noise capability of our terahertz-spectroscopy technique permits accurate measurement of power transmission coefficients less than 0.001 (absorption coefficients >5000 cm−1) and index variations larger than λ(dn/dλ) > 44, as demonstrated by the accurate fit of our data through the Reststrahlen region of CdTe.