Using nanoindentation techniques, the mechanical properties of amorphous Al2O3 thin films with oxide thicknesses ranging from approximately 3 nm (native oxides) to 360 nm on substrates of polycrystalline Al and single crystals of sapphire and silicon have been investigated. The measured composite hardness as a function of the ratio of the indentation depth and the film thickness was compared with predictions of existing phenomenological models based on laws of mixture of the area or volume fractions. When the parameters are adjusted, these models can predict the measured hardness vs. indentation depth either for a hard film on a soft substrate or a soft film on a hard substrate. None of the models describes both cases. A new model based on a law of volume fractions is presented which, with relevant physical parameters, describes both cases; except for the thinnest films on soft substrates, where the discrepancy is assumed to be connected with a membrane-like deformation of the film.