The ability to tune the iron chalcogenides
BaFe
2
Q
3
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
BaFe
2
Q
2
O
(
Q
=
S
,
Se
)
and show that their magnetic behavior results from nearest-neighbor magnetic exchange interactions via oxide and selenide anions of similar strength, with properties consistent with more localized electronic structures than those of
BaFe
2
Q
3
systems.