Fiber-reinforced materials exhibit interesting size effects due to the material contrast between fiber andmatrix materials and the slenderness of the fibers. Homogenization theory cannot account for such ef-fects when considering standard Cauchy continua. Multiphase continuum models [1, 2] are a class ofgeneralized continua which consist of different media (fiber and matrix phases) possessing their ownkinematics and in interaction with each other. An interaction energy depending on the difference of bothphases displacements is at the origin of a size effect. Moreover, different boundary conditions can beprescribed at the same point for each phase, enabling to simulate, at the macroscopic level, matrix cracksbridged by intact fibers.We will describe a homogenization procedure for deriving the generalized material parameters in theelastic setting. This procedure will be then validated by comparing against finite-element computationson the heterogeneous structure. Finally, by considering a damage model for the matrix and the interface,we will show that regular microcracking can be obtained using this generalized continuum model