Various numerical models have been developed for the analysis of damage phenomena in bioinspired microstructures, including those based on nonlinear homogenization techniques or, more generally, on multiscale approaches. However, many of these approaches still require high computational costs, since they adopt time-consuming computational homogenization approaches. The present work aims to propose a computationally efficient hierarchical multiscale strategy for the investigation of damage phenomena in bioinspired composite structures. Such a strategy relies on a combined continuous/discontinuous homogenization technique, which allows to overcome the well-known mesh sensitivity issues occurring after the appearance of strain localization events. In detail, the proposed multiscale model uses a complete homogenized stress-strain database obtained for a Repeating Unit Cell (RUC) subjected to several macroscopic strain histories. Then, a macroscopic interfacial constitutive law is extracted from such a database “on-the-fly”, i.e. during the multiscale simulation. Finally, the proposed multiscale damage model is validated for nacre-like bioinspired composites via suitable comparisons with direct numerical simulations, with reference to complex failure mechanisms.