We employ a novel spectroscopic setup based on an external cavity quantum cascade laser and a MachZehnder interferometer to simultaneously record spectra of absorption and dispersion of liquid samples in the mid-infrared. We describe the theory underlying the interferometric measurement and discuss its implications for the experiment. The capability of simultaneously recording a refractive index and absorption spectrum is demonstrated for a sample of acetone in cyclohexane. The recording of absorption spectra is experimentally investigated in more detail to illustrate the methods capabilities as compared to direct absorption spectroscopy. We find that absorption signals are recorded with strongly suppressed background, but with smaller absolute sensitivity. A possibility of optimizing the setups performance by unbalancing the interferometer is presented.