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Interlayer exchange coupling has been studied in a series of [Pt( tPt Å)/Co(4 Å)]n/NiO( tNiO)/[Co(4 Å)/Pt( tPt Å)]n multilayers with perpendicular anisotropy. The coupling oscillates between antiferromagnetic and ferromagnetic as a function of tNiO with a period of ~5 Å, and the oscillatory behavior is related to the antiferromagnetic ordering of the NiO layer. This interlayer coupling between two Co/Pt multilayers is shown to occur domain by domain by magnetic force microscopy imaging. For the strongest antiferromagnetic coupling at tNiO = 11 Å, an oscillation with a period of ~6 Å is superposed onto the exponential decay of the coupling strength as a function of tPt. The exponential decay with tPt is ascribed to the exponential decay of the coupling between the Co layers across the Pt layers in each Co/Pt multilayer, and the superposed oscillatory behavior can be attributed to multiple reflections of electron waves at the Co/Pt interfaces and their interference. A linear dependence of the antiferromagnetic coupling strength on 1/n, (where n is the number of repeats), is suggestive of a surface interaction for this interlayer coupling.