Hybrid masonry is a relatively new type of structural system that benefits from the ductility and ease of construction of steel frames and from the in-plane strength and stiffness of reinforced masonry panels. Finite element analyses of hybrid masonry systems employ complex models, such as the two-scalar continuum damage model, to capture the propagation of damage through the masonry panels. Such formulations rely on several constitutive parameters but no simple experiments exist that can be used to decouple their effect and calibrate them independently. This paper proposes a method to calibrate the masonry parameters using experimental data from global system testing. Steel components are described by an elastoplastic model with kinematic hardening whose constitutive parameters are easily calibrated. A parameter calibration procedure for the damage model parameters based on the behavior of the base wall of a two-story hybrid system in global testing is proposed. In order to reduce the number of calibrated parameters, two constraints are applied to the compressive range of the constitutive law, requiring that for that range the stress-strain curve is similar to that of concrete. The effectiveness of these two constraints in finding an optimized set of parameters more efficiently is then verified by using uniaxial compression test data. An automatic calibration procedure of the remaining parameters is proposed based on the Nelder-Mead simplex method. It is demonstrated through numerical experiments that the models with calibrated parameters can accurately capture the behavior of hybrid masonry systems.