This Letter presents a dispersion spectroscopy method that achieves simultaneous detection of molecular vibrational dispersion over a broad spectral range. The method is implemented with an infrared mode-locked laser, a dispersion-compensated Michelson interferometer, and a multichannel detector. Synchronous detection under interferometric phase modulation near the destructive interference condition is employed to achieve a high signal-to-noise ratio. We successfully demonstrate the method by measuring the dispersion of carbon monoxide gas, achieving a noise-equivalent dispersion of 1.3 × 10-8 cm and a corresponding noise-equivalent absorbance of 6.5 × 10-4 with a measurement time of 2.2 s.