The contribution at hand introduces a novel formulation that couples the Material Point Method (MPM) and Finite Element Method (FEM) based on nonlocal mechanics using an implicit time integration scheme. A constitutive formulation at finite deformations to describe fiber-reinforced concrete is applied. A damage approach within the microplane framework is utilized to capture the induced anisotropy in concrete structures. Furthermore, the microplane model is able to capture the initial anisotropy due to fiber inclusion. In addition, an implicit gradient enhancement is utilized to overcome problems of numerical instabilities when modeling softening phenomena. Numerical examples are presented to demonstrate the capability of this new approach to couple the mechanical and nonlocal fields between MPM and FEM in a reliable and physical manner.