High sensitivity of spectroscopic ellipsometry and reflectometry for the characterization of thin films can strongly decrease when layers, typically metals, absorb a significant fraction of the light. In this paper, we propose a solution to overcome this drawback using total internal reflection ellipsometry (TIRE) and exciting a surface longitudinal wave: a plasmon-polariton. As in the attenuated total reflectance technique, TIRE exploits a minimum in the intensity of reflected transversal magnetic (TM) polarized light and enhances the sensitivity of standard methods to thicknesses of absorbing films. Samples under study were stacks of three films, ZnO : Al/Ag/ZnO : Al, deposited on glass substrates. The thickness of the silver layer varied from sample to sample. We performed measurements with a UV-visible phase-modulated ellipsometer, an IR Mueller ellipsometer and a UV-NIR reflectometer. We used the variance-covariance formalism to evaluate the sensitivity of the ellipsometric data to different parameters of the optical model. Results have shown that using TIRE doubled the sensitivity to the silver layer thickness when compared with the standard ellipsometry. Moreover, the thickness of the ZnO : Al layer below the silver layer can be reliably quantified, unlike for the fit of the standard ellipsometry data, which is limited by the absorption of the silver layer.