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This paper proposes interface and polynomial enrichments using the generalized finite element method (IGFEM) for the material interface in composite materials without matching the finite element mesh to the boundaries of different materials. Applications in structural members such as laminated beams and heterogeneous composites (matrix and inclusions) employing coarse and fine meshes are employed. The results were compared with conventional GFEM and analytical solutions. Verification and simulations proved the efficiency of the suggested framework for solving problems with discontinuous gradients resulting from a material interface. The proposed method allows flexibility in mesh generation for composite materials by letting the interface be embedded in an element without the need to match the mesh to the material interface. This improves the computational efficiency over conventional methods.