Terahertz quantum cascade lasers (QCLs) have been used together with a monolithic planar Schottky diode receiver to study the heterodyne mixing between dual internal modes of a QCL and between a single mode of a QCL and a known molecular line from a molecular gas laser. Dual-mode mixing shows that I e intrinsic linewidth of a free-running QCL is <= 30 kHz. Mixing against a molecular laser line gives a high precision measurement of a QCL's absolute frequency and can show transient turn-on behavior in a pulsed QCL.