Interference microscopy is a widely used technique in optical metrology for the characterization of materials and in particular for measuring the micro and nanotopography of surfaces. Depending on the processing applied to the interference signal, either topographic analysis of the sample can be carried out by identifying the envelope peak of the fringe signal, which leads to 3D surface imaging, or spectral analysis may be performed which gives spectroscopic measurements. By applying a Fourier transform to the interference fringes, information about the source spectrum, the spectral response of the optical system, and the reflectance spectrum of the surface at the origin of the interferogram can be obtained. By using a sample of known reflectivity for calibration, it is possible to extract the spectral signature of the entire system and therefore to deduce that of the surface of interest. In this paper, we first explain theoretically how to retrieve the reflectance information of a surface from the interferometric signal. Then, we present some results obtained by this means with a white light scanning Linnik interferometer on different kinds of samples (silicon, tin oxide (SnO2), indium tin oxide (ITO)). The initial results were slightly different from those obtained with a conventional optical spectrometer until averaged temporally and were improved even further when averaged spatially. We show that the reflectance of the surface can be calculated over the given wavelength range of the effective spectrum, which is defined as the source spectrum multiplied by the spectral response of the camera and the spectral transmissivity of the optical system. We thus demonstrate that local spectroscopic measurements can be carried out with an interference microscope and that they match well with those measured with an optical spectrometer model Lambda19 UV-VIS-NIR from Perkin Elmer. A simulation study is also presented in order to validate the method and to help identify the potential sources of errors in the spectroscopic analysis.