This paper is devoted to the analysis of the homogenized behavior of unidirectional composite materials once the fibers are debonded from (but still in contact with) the matrix. This homogenized behavior is built by an asymptotic method in the framework of the homogenization theory. The main result is that the homogenized behavior of the debonded composite is that of a generalized continuous medium with an enriched kinematics. Indeed, besides the usual macroscopic displacement field, the macroscopic kinematics contains two other scalar fields. The former one corresponds to the displacement of the matrix whereas the two latter ones correspond to the sliding and the rotation of the debonded fibers with respect to the matrix. Accordingly, new homogenized coefficients and new coupled equilibrium equations appear. This problem is addressed in a linear elastic three-dimensional setting.