The optical properties of thin films are generally determined by direct photometric quantities. We show that additional insight into the properties of anisotropic thin films can be obtained by computing the polarization eigenstates and eigenvalues of their Jones matrices. We consider helically structured thin films, which display intriguing optical response, such as the circular Bragg resonance. Using numerical simulations and actual measurements, we show that the eigenvectors are mutually orthogonal in most regions of the wavevector space, except near the circular Bragg and the oblique resonances. Special wavevector values, called exceptional points, are found where the Jones matrix becomes defective and its eigenvectors coalesce. Exceptional points are also found in pairs of wavevector values differing only by a sample rotation by π around the direction normal to the sample; this property is shown to arise from Saxton - de Hoop's reciprocity principle, which applies to lossy materials and contains time reversal symmetry, which only applies to lossless materials, as a special case.