The ability to tune the iron chalcogenides BaFe2Q3 from Mott insulators, to metals and then superconductors with applied pressure has renewed interest in low-dimensional iron chalcogenides and oxychalcogenides. We report here a combined experimental and theoretical study on the iron oxychalcogenides BaFe2Q2O (Q=S, Se) and show that their magnetic behaviour results from nearest-neighbour magnetic exchange interactions via oxide and selenide anions of similar strength, with properties consistent with more localised electronic structures than those of BaFe2Q3 systems.