We present a systematic Monte Carlo and numerical self-consistent field (NSCF) study of thin films consisting of grafted and free polymers in good solvent, for the range of densities found in most experiments. Above the overlap threshold for the grafted polymer, the two approaches agree well. Even at low densities, the agreement is surprisingly good. The NSCF results are also directly compared with experiments. The systematic results are interpreted in the context of the regimes and behavior predicted by scaling and analytic SCF theories. We find that the grafted layer is generally thinner, and the penetration of the free polymer into the grafted layer is generally greater than predicted, and that the overall behavior is not in accord with the earlier theories. We find it useful to introduce and distinguish between two measures of the penetration, and we find that one of them can increase with the concentration of grafted polymer.