The mechanical properties of a unidirectional carbon-fiber reinforced polymer (CFRP) laminate with Cu mesh layers were investigated for use in aerospace applications as a multifunctional structural and electromagnetic interference shielding component. Nanoindentation was used to study the fiber/PEEK and Cu/PEEK interfaces. A data analysis methodology is presented to assess the interfacial strength from plots of hardness and modulus versus distance from fiber/Cu edge. The results indicated that annealing resulted in enhanced adhesion at the fiber/PEEK interface. Additionally, indents near the Cu/PEEK interface indicated poor interfacial adhesion. Bulk mechanical testing was performed to determine the effect of adding Cu mesh layers on the mechanical properties of the laminate. Additional Cu mesh layers decreased the tension, shear, and bending strength/modulus, while the open hole compression strength increased. This indicates that the Cu/PEEK interfaces weaken the laminate and lower the tension, shear, and bending strength by delamination.