We propose a laser feedback interferometer operating at multiple terahertz (THz) frequency bands by using a pulsed coupled-cavity THz quantum cascade laser (QCL) under optical feedback. A theoretical model that contains multi-mode reduced rate equations and thermal equations is presented, which captures the interplay between electro-optical, thermal, and feedback effects. By using the self-heating effect in both active and passive cavities, self-mixing signal responses at three different THz frequency bands are predicted. A multi-spectral laser feedback interferometry system based on such a coupled-cavity THz QCL will permit ultra-high-speed sensing and spectroscopic applications including material identification.