Molecular dispersion spectroscopy encompasses a group of spectroscopic techniques for gas analysis that retrieve the characteristics of the sample from the measurement of the profile of its refractive index in the vicinity of molecular resonances. This approach, which is in clear contrast to traditional methods based on the detection of absorption, provides inherent immunity to power fluctuations, calibration-free operation, and an output that is linearly dependent on gas concentration. Heterodyne phase-sensitive dispersion spectroscopy (HPSDS) is a very recently proposed technique for molecular dispersion spectroscopy based on tunable lasers that is characterized by a very simple architecture in which data processing and concentration retrieval are straightforward. Different HPSDS implementations have been experimentally validated in the near-IR. Here, we present the first demonstration of HPSDS in the mid-IR using a directly modulated quantum cascade laser for the measurement of CO. The setup is put under test to characterize its response to changing concentrations, pressures, and levels of optical intensity on the detector, and the limit of detection is estimated. Besides this, an experimental comparison with wavelength modulation spectroscopy with second-harmonic detection (2f-WMS) is performed and discussed in detail in order to offer a clear view of the benefits and drawbacks that HPSDS can provide over what we could consider the reference method for gas analysis based on tunable laser spectroscopy.