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The structures of equimolar mixtures of the commonly used polar aprotic solvents dimethylformamide (DMF) and dimethylacetamide (DMAc) in dimethylsulfoxide (DMSO) have been investigated via neutron diffraction augmented by extensive hydrogen/deuterium isotopic substitution. Detailed 3-dimensional structural models of these solutions have been derived from the neutron data via Empirical Potential Structure Refinement (EPSR).The intermolecular Centre-of-Mass (CoM) distributions show that the first coordination shell of the amides comprises 13-14 neighbours, of which approximately half are DMSO. In spite of this near ideal coordination shell mixing, the changes to the amide-amide structure are found to be relatively subtle when compared to the pure liquids. Analysis of specific intermolecular atom-atom correlations allows quantitative interpretation of the competition between weak interactions in solution. We find a hierarchy of formic and methyl C-H to O hydrogen bonds form the dominant local motifs, with peak positions in the range 2.5-3.0 Å. We also observe a rich variety of steric and dispersion interactions, including those involving the amide pi-backbones. This detailed insight into the structural landscape of these important liquids demonstrates the versatility of DMSO as a solvent and the unparalleled resolution of neutron diffraction, which is critical for understanding weak intermolecular interactions at the nanoscale and thereby tailoring solvent properties to specific applications.