Co/Cu multilayers were prepared by cross-beam pulsed laser deposition and characterised by high-angle X-ray diffraction as well as specular and off-specular reflection before and after annealing (500 degreesC, 2 h). Using synchrotron radiation at the K-edge energy of Co and Cu to enhance the scattering contrast, the study shows that annealing does not enlarge the interface roughness, sigma(r.m.s), but strongly influences the interface morphology. In the fractal model of self-affine structures the latter is expressed by the drastic reduction of the extremely large lateral roughness correlation length parameter, xi, from approximately 4 mum in the as-deposited state to approximately 20 mm after annealing. High-angle X-ray diffraction indicates that the reduction of xi is caused by grain coarsening due to growth of crystallites and grain boundaries. Thermal treatment enhances the separation of Co and Cu at the interface, i.e. the initially very jagged (roughness exponent, It, between 0.15 and 0.3) structure is smoothed (It between 0.6 and 0.7).