Some recent works dealing with damage in long-fiber laminates have proposed the idea of building a bridge between micromodeling on the fiber's scale and mesomodeling on the ply's scale. The numerical form of these micro-meso relations enables one to define the domains of quasi-equivalence and nonequivalence between micro- and mesomodeling. We propose a first improvement in order to increase the confidence in mesomodeling under outof-plane solicitations like edge zone and low velocity impact. Usually, continuum damage mechanics approaches do not account satisfactorily for the interactions between ply damage and interface damage. These interactions, which are naturally modeled on the microscale, are transferred to the mesoscale through the micro-meso bridge. After several pragmatic choices, the result of the homogenization is an orthotropic, non-local interface model whose behavior depends on the damage mesovariables of the adjacent plies.