We demonstrate high-sensitivity vibrational absorption spectroscopy in the 2-micron wavelength range by using a mode-locked Cr:ZnS laser. Interferometric subtraction and multichannel detection across the broad laser spectrum realize simultaneous background-free detection of multiple vibrational modes over a spectral span of >380 cm-1. Importantly, we achieve detection of small absorbance on the order of 10-4, which is well below the detection limit of conventional absorption spectroscopy set by the detector dynamic range. The results indicate the promising potential of the background-free method for ultrasensitive and rapid detection of trace gases and chemicals.