In this paper an interface model accounting for roughness and micro-cracks is presented and applied to masonry-like structures. The model is consistently derived by coupling a homogenization approach and arguments of asymptotic analyses. A numerical procedure is introduced and numerical results, based on a finite element formulation, are successfully compared with experimental data , obtained on masonry samples undergoing to shear tests. Finally, a parametric numerical analysis is proposed, highlighting the influence of the roughness features on the interface response.