Nonlinear phase dispersion spectroscopy is introduced as a means to retrieve wideband, high spectral resolution profiles of the wavelength-dependent real part of the refractive index. The method is based on detecting dispersion effects imparted to a light field with low coherence transmitted through a thin sample and detected interferometrically in the spectral domain. The same sampled signal is also processed to yield quantitative phase maps and spectral information regarding the total attenuation coefficient using spectral-domain phase microscopy and spectroscopic optical coherence tomography (SOCT), respectively. Proof-of-concept experiments using fluorescent and nonfluorescent polystyrene beads and another using a red blood cell demonstrate the ability of the method to quantify various absorptive/dispersive features. The increased sensitivity of this method, novel to our knowledge, is compared to intensity-based spectroscopy (e.g., SOCT), and potential applications are discussed.