We report the complex refractive index of methylammonium lead iodide (CH3NH3PbI3) perovskite thin films obtained by means of variable angle spectroscopic ellipsometry and transmittance/reflectance spectrophotometry in the wavelength range of 190 nm to 2500 nm. The film thickness and roughness layer thickness are determined by minimizing a global unbiased estimator in the region where the spectrophotometry and ellipsometry spectra overlap. We then determine the optical bandgap and Urbach energy from the absorption coefficient, by means of a fundamental absorption model based on band fluctuations in direct semiconductors. This model merges both the Urbach tail and the absorption edge regions in a single equation. In this way, we increase the fitting region and extend the conventional (αℏω)2-plot method to obtain accurate bandgap values.