A technique is formulated to determine both thickness and refractive indices of free-standing films with biaxial symmetry from polarized transmission spectra. The films must be transparent and show little dispersion in refractive indices in the wavelength range where the transmission spectra are collected. Methods are proposed to correct the errors caused by imperfect polarization of incident radiation and thickness variation across the sampling area. Anisotropic refractive indices and thickness of poly(biphenyl dianhydride-p-phenylenediamine) films which exhibit uniaxial optical anisotropy are determined from polarized transmission spectra. The refractive index and thickness values compare well to those obtained from waveguide prism coupler and profilometer measurements.