We demonstrate coherent averaging of the multi-heterodyne beat signal between two quantum cascade laser frequency combs in a master-follower configuration. The two combs are mutually locked by acting on the drive current to control their relative offset frequency and by radio-frequency extraction and injection locking of their intermode beat signal to stabilize their mode spacing difference. By implementing an analog common-noise subtraction scheme, a reduction of the linewidth of all heterodyne beat notes by five orders of magnitude is achieved compared to the free-running lasers. We compare stabilization and post-processing corrections in terms of amplitude noise. While they give similar performances in terms of signal-to-noise ratio, real-time processing of the stabilized signal is less demanding in terms of computational power. Lastly, a proof-of-principle spectroscopic measurement was performed, showing the possibility to reduce the amount of data to be processed by three orders of magnitude, compared to the free-running system.