Three new NaBa2M3Q3(Q2) (M = Ag or Cu; Q = S or Se) chalcogenides were prepared by using solid-state methods and structurally characterized by using single-crystal X-ray diffraction. NaBa2Ag3Se3(Se2) and NaBa2Cu3Se3(Se2) crystallize in monoclinic space group C2/m and have a two-dimensional structure composed of edge-sharing MSe4/4 tetrahedra separated by Na+ and Ba2+ cations, along with (Se2)2- dimers at the center of the spacings between [M3Se3]3- slabs. NaBa2Ag3S3(S2) adopts a related structure with space group C2/m but has additional, crystallographically distinct Ag atoms in the [Ag3S3]3- layer that are linearly coordinated. NaBa2Ag3Se3(Se2) and NaBa2Ag3S3(S2) have indirect band gaps measured to be 1.2 and 1.9 eV, respectively, which is supported by band structures calculated using density functional theory. Mixed-anion NaBa2Cu3Se5-xSx compositions were prepared to probe the presence of anion ordering and heteronuclear (S-Se)2- dimers. Structural analyses of the sulfoselenides indicate that selenium preferentially occupies the Q-Q dimer sites, while Raman spectroscopy reveals a mixture of (S2), (Se2), and heteronuclear (S-Se) units in the sulfur-rich products. The local ordering of the chalcogens is rationalized using simple bonding concepts and adds to a growing framework for understanding ordering phenomena in mixed-anion systems.