  We devise a new detection technique for mid-infrared multi-heterodyne
spectroscopy. As an experimental implementation, mid-infrared light
interrogates a gas sample in the 3-$\mu$m region of the fundamental CH, OH, NH
stretch in molecules and detection is performed in the near-infrared
telecommunication region. Spectra showing 18000 resolved comb lines of 100-MHz
spacing are recorded at a sensitivity close to the shot-noise limit. The
demonstration adds to the unique advantages of dual-comb spectroscopy, such as
potential very high resolution, negligible instrumental line width, and direct
calibration of the frequency scale with an atomic clock. We also show that
direct mid-infrared detection with a differential photo-detector module is
beneficial in the limit of low mid-infrared average power.
