We demonstrate the use of white-light spectral interferometry as an effective technique involving only linear optical interactions and a partially coherent light source to measure the complex transmission response function of optical resonance and to determine the corresponding variation in the refractive index relative to a reference. We also discuss experimental arrangements to increase the accuracy and sensitivity of the technique. The superiority of the technique over single-beam absorption measurements is demonstrated by the accurate determination of the response function of the chlorophyll-a solution. The technique is then applied to chlorophyll-a solutions of varying concentrations and gold nanocolloids to characterize inhomogeneous broadening. Results on the inhomogeneity of gold nanocolloids are also supported by transmission electron micrographs, showing distributions of the size and shape of the constituent gold nanorods.