We describe our phase-sensitive interferometry technique implemented as phase dispersion microscopy (PDM)/optical tomography (PDOT). The technique is based on measuring the phase difference between fundamental and second harmonic low coherence light in a novel interferometer. We attain high sensitivity to subtle refractive index differences due to dispersion with a differential optical path sensitivity of 5 nm. Using PDM, we show that ballistic light in a turbid medium undergoes a phase velocity change that is dependent on scatterer size. We demonstrate that the microscopy technique performs better than a conventional phase contrast microscope in imaging dispersive and weakly scattering samples. The tomographic implementation of the technique (PDOT) can complement Optical Coherence Tomography (OCT) by providing phase information about the scanned object.