A dispersive white-light spectral interferometer for precise measurements of the phase properties of multilayer thin film structures is built. A novel wavelet-based differentiation approach that considerably resists measurement error of group delay (GD) and group delay dispersion (GDD) is introduced. Versatile applications beyond phase measurement of the apparatus are demonstrated, including piezoelectric coefficient determination and physical thickness retrieval. With the increase of demand for thin film structures with specific phase properties, this white-light spectral interferometer can play an important role in future thin film industry.