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Optical frequency combs generated by quantum cascade lasers have recently been demonstrated in the mid and far infrared, but a detailed analysis of the possibility of a fine control of the emission to use them for high-resolution spectroscopy and metrology applications is still missing. In this manuscript the attempt of frequency stabilizing a mid-infrared quantum cascade laser comb (QCL-comb) against a metrological mid-infrared intracavity-difference-frequency-generated comb through a single phase-locking chain acting on the driving current is presented. Following a brief derivation, simple relations between the QCL-comb frequency parameters and optical quantities such as the refractive index have been found and used to observe how the locking affects the physics of the system. The conclusion is that the current locking essentially acts on the effective refractive index to reduce the offset fluctuations (common noise), but does not sensitively affect the group refractive index and the mode spacing. Nonetheless, the overall single QCL-comb tooth linewidth is reduced from 500kHz down to values ranging from 1 to 23kHz on a 40ms time scale.