We carry out wavelength-dependent second harmonic interference experiments using thin films of an organic dye as nonlinear optical sources. While the measured difference of refractive index between the fundamental and second harmonic wavelengths follows the theoretical expectation for air in a wide spectral region, anomalous dispersion is observed when the second harmonic light lies in the absorption band of the dye. The sensitivity of the technique to small refractive index variations may prove useful for sensing applications as well as for testing models of light dispersion in weakly dispersing and absorbing media.