The theoretical investigation of sum and difference frequency generation in thin surface layers with rotational symmetry leads to formulas which connect the generated light intensities to the surface second order nonlinear susceptibility tensor. A maximum of seven tensor components can be determined in the case of lowest symmetry. Measurements in transmission should be especially useful since they allow easy variation of both polarization and angle of incidence. On the other hand, large signal enhancements are expected for total internal reflection geometries. A consistent set of χ(2) tensor components for a thin layer of rhodamine-6G adsorbed on fused silica is found based on data from reflection and transmission measurements.