We demonstrate a common-path optical interferometer based on a quantum-cascade laser (QCL), in which the QCL acts both as source and detector of the infrared radiation. The collinear arms of the interferometer are terminated by a plastic surface (acting as the beam splitter) and by a metallic one (acting as the mirror). The different reflectivity of the surfaces allows for high contrast feedback-interferometry fringes exhibited on the laser-emitted power and revealed by voltage compliance measurement at the QCL terminals. The displacement of each surface can be identified and measured with sub wavelength resolution. The experimental results are in excellent agreement with the numerical simulations based on the Lang-Kobayashi model for multiple cavities. Applications to microfluidics and resonant chemical detection can be envisaged.