The structure of xAs40Se60-(1 - x)As40S60 glasses, where x = 1.000, 0.667, 0.500, 0.333, 0.250, and 0.000, is investigated using a combination of neutron and X-ray diffraction coupled with computational modeling using multicomposition empirical potential structure refinement (MC-EPSR). Traditional EPSR (T-EPSR) produces a set of empirical potentials that drive a structural model of a particular composition to agreement with diffraction experiments. The work presented here establishes the shortcomings in generating such a model for a ternary chalcogenide glass composition. In an enhancement to T-EPSR, MC-EPSR produces a set of pair potentials that generate robust structural models across a range of glass compositions. The structures obtained vary with composition in a much more systematic way than those taken from T-EPSR. For example, the average arsenic-sulfur bonding distances vary between 2.28 and 2.46 Å in T-EPSR but are 2.29 ± 0.02 Å in MC-EPSR. Similarly, the arsenic-selenium bond lengths from T-EPSR vary between 2.28 and 2.43 Å but are consistently 2.40 ± 0.02 Å in the MC-EPSR results. Analysis of these models suggests that the average separation of the chalcogen (S or Se) atoms is the structural origin of the changes in nonlinear refractive index with glass composition.