The terahertz region is of great importance for spectroscopy since many molecules have absorption fingerprints there. Frequency combs based on terahertz quantum cascade lasers feature broadband coverage and high output powers in a compact package, making them an attractive option for broadband spectroscopy. Here, we demonstrate the first multiheterodyne spectroscopy using two terahertz quantum cascade laser combs. Over a spectral range of 250 GHz, we achieve average signal-to-noise ratios of 34 dB using cryogenic detectors and 24 dB using room-temperature detectors, all in just 100 µs. As a proof of principle, we use these combs to measure the broadband transmission spectrum of etalon samples and show that, with proper signal processing, it is possible to extend the multiheterodyne spectroscopy to quantum cascade laser combs operating in pulsed mode. This greatly expands the range of quantum cascade lasers that could be suitable for these techniques and allows for the creation of completely solid-state terahertz laser spectrometers.