Reflection electron microscopy of electrodeposited Co, Cu/(111) Pt ultrathin layers and bilayers has revealed a heteroepitaxial and simultaneous multinuclear multilayer growth. "Giant" magnetoresistance and oscillatory antiferromagnetic interlayer coupling have been observed in a (111) textured Co/Cu multilayered nanostructure, which is compositionally modulated over nanometer length scales with distinct ferromagnetic Co-Cu alloy and nonmagnetic Cu layers, prepared by electrodeposition under potential control in the presence of a very slight amount of CrO3. Such a multilayered structure containing a nominal Cu spacer layer thickness of 3.2 nm exhibits a large saturation magnetoresistance of more than 18% at room temperature.