We present a new measurement technique based on second-harmonic generation to investigate thin molecular films with in-plane anisotropy. The technique does not rely on continuous azimuthal patterns of the second-harmonic intensities. Instead, the second-harmonic intensities are recorded at a number of selected distinct azimuthal orientations of the sample. The signals are recorded as functions of the state of polarization of the fundamental laser beam. Only normalized polarization line shapes are required. As the line shapes need not be mutually calibrated, the technique is limited only by the accuracy of the individual polarization measurements and is applicable also to samples with inhomogeneous surface coverage of molecules. The technique is applied to anisotropic chiral thin films with C-2 symmetry made of helicenebisquinone. Full analysis of the nonlinear susceptibility tensor of the samples is performed and the effects of anisotropy and chirality separated. The part of the nonlinearity arising from chirality is shown to dominate the nonlinear response.