Several bioinspired composites exhibit superior mechanical properties compared to the common engineering materials by virtue of their highly organized, heterogeneous microstructure, usually spanning several length scales. Examples of these architectured materials are inspired by bone, wood, and nacre. Several modelling approaches have already focused on investigating the mechanical behavior of bioinspired materials. However, most of these approaches are computationally costly. This work presents an efficient hierarchical multiscale model based on a combined bulk/interface homogenization technique to investigate anisotropic damage in bioinspired microstructures. Its main advantage is to overcome the well-known mesh sensitivity problems experienced by purely continuous classical homogenization techniques in the presence of strain localization. A Diffuse Interface Model is here used for describing arbitrary macroscopic cracks, which relies on the insertion of interelement interfaces equipped with a microscopically informed cohesive traction-separation law, extracted “on-the-fly” from the nonlinear homogenized response of a Representative Volume Element. The proposed model is applied to the failure analysis of a nacre-like composite beam and validated via comparisons with a direct numerical simulation.