Two different laminated composites with submicron-scale grain size and strong interface bonding toughness, Cu/Al and Cu/Cu, were fabricated by cold-roll bonding at ambient temperature, and then annealing of the laminated composites was conducted to get different interface bonding toughness. It was found that a better strength-plasticity combination for the laminated composites could be obtained through stronger interface bonding toughness, which effectively delayed the onset of plastic instability and premature local necking of the material. Uniform elongation of both Cu/Al and Cu/Cu laminated composites was enhanced compared with that of the cold-rolled Cu. At the same strength level, plasticity of the Cu/Cu laminated composite is better than that of the Cu/Al one and that of the cold-rolled Cu. Mechanisms of plasticity instability and fracture of the laminated composites were evaluated.