Aims. Properly characterizing Fabry-Perot interferometers (FPI) is essential for determining their effective properties and evaluating the performance of the astronomical instruments in which they are employed. Furthermore, in two-dimensional spectrographs where multiple FPI are used in series, the actual distribution of plate separation errors will be crucial for determining the resulting transmission profiles. We describe techniques that address these issues utilizing the FPI of IBIS, a solar bidimensional spectrometer installed at the Dunn Solar Telescope. Methods. A frequency-stabilized He-Ne laser was used in three different optical layouts to measure the spatially-resolved transmission of the FPI. Analyzing the shape and wavelength shift of the observed profiles allows the characteristics of the cavity errors and the interferometer coating to be determined. Results. We have measured the spatial distribution of the large-scale plate defects, which shows a steep radial trend, as well as the magnitude of the small-scale microroughness. We also extracted the effective reflectivity and absorption of the coating at the laser line wavelength for both interferometers. Conclusions. These techniques, which are generally applicable to any Fabry-Perot interferometer, provide the necessary information for calculating the overall instrumental profile for any illuminated area of the interferometer plates. Accurate knowledge of the spectral transmission profile is important, in particular when using inversion techniques or in comparing observations with simulated data.