First principles band structure calculations have been performed for (110) and (100) Fe/Cr and Fe/V superlattices with mixed monolayers at the interfaces, with atomic concentrations in the mixed layers throughout the entire concentration range. In addition, (211) and (111) superlattices with perfect interfaces have been studied. For Fe/V systems the moments at the interfaces depend strongly on the nearest neighbour environment. Conversely, Fe and Cr moments at Fe/Cr interfaces show almost no dependence on the nearest neighbour environment. We explain the latter behaviour as the result of competing antiferromagnetic exchange interactions at the interface, and discuss why this behaviour is crucial to the strong spin dependence of scattering at Fe/Cr interfaces, which gives rise to the very large giant magnetoresistance effect observed for Fe/Cr multilayers. Implications are given for the temperature dependence of the GMR ratio.