We report simulations of nonlinear optical transmission of an optical beam through heterogeneous metallodielectric stacks under the action of nonlinear absorption. We use the finite element method (FEM) with two-dimensional transverse effects and transfer matrix method simulation techniques as complementary methods to validate the FEM approach. We find a significant nonlinear absorption effect across spectral regimes where transmission is high. We compare the results with energy and group velocity results, but the enhancement of the nonlinear response is attributed to field confinement in the metal layers.