A simple formulation for the indentation stress-strain behavior of bilayers in contacts with hard spheres is proposed. The formulation is based on empirical power-law stress-strain relations for each of the individual constituent bulk materials, acid thence for the bilayer coating/substrate composite. For the constituent materials, two regions of response are considered : at low loads, an elastic region, with linear stress-strain response (exponent = 1); at high loads, an elastic-plastic region, with nonlinear stress-strain response (exponent < 1). The material responses in each of these two regions are characterized by effective moduli. For the composite bilayer, the transition in load-bearing capacity from coating to substrate with increasing load is represented by a three-parameter Weibull asymptotic function of ratio contact radius to coating thickness. This function conveniently defines the geometrical aspects of the contact response separately from the material properties. The power-law formulation is tested, and the Weibull parameters calibrated, against FEM-generated and experimental indentation stress-strain data for selected coating/substrate systems with widely different interlayer elastic-plastic mismatch. The formulation allows a priori predictions of the composite bilayer indentation stress-strain curves from control data on the constituent materials. Conversely, measurements of indentation stress-strain responses on given bilayers may be used to evaluate otherwise undeterminable elastic-plastic properties of coatings on well-characterized substrates.