New fluorinated hybrid solids [Mo2F2O5(tr2pr)] (1), [Co3(tr2pr)2(MoO4)2F2]·7H2O (2), and [Co3(H2O)2(tr2pr)3(Mo8O26F2)]·3H2O (3) (tr2pr = 1,3-bis(1,2,4-triazol-4-yl)propane) were prepared from the reaction systems consisting of Co(OAc)2/CoF2 and MoO3/(NH4)6Mo7O24, as Co(II) and Mo(VI) sources, in water (2) or in aqueous HF (1, 3) employing mild hydrothermal conditions. The tr2pr ligand serves as a conformationally flexible tetradentate donor. In complex 1, the octahedrally coordinated Mo atoms are linked in the discrete corner-sharing {Mo2(μ2-O)F2O4N4} unit in which a pair of tr-heterocycles (tr = 1,2,4-triazole) is arranged in cis-positions opposite to "molybdenyl" oxygen atoms. The anti-anti conformation type of tr2pr facilitates the tight zigzag chain packing motif. The crystal structure of the mixed-anion complex salt 2 consists of trinuclear [Co3(μ3-MoO4)2(μ2-F)2] units self-assembling in Co(II)-undulating chains (Co···Co 3.0709(15) and 3.3596(7) Å), which are cross-linked by tr2pr in layers. In 3, containing condensed oxyfluoromolybdate species, linear centrosymmetric [Co3(μ2-tr)6](6+) SBUs are organized at distances of 10.72-12.45 Å in an α-Po-like network using bitopic tr-linkers. The octahedral {N6} and {N3O3} environments of the central and peripheral cobalt atoms, respectively, are filled by triazole N atoms, water molecules, and coordinating [Mo8O26F2](6-) anions. Acting as a tetradentate O-donor, each difluorooctamolybdate anion anchors four [Co3(μ2-tr)6](6+) units through their peripheral Co-sites, which consequently leads to a novel type of a two-nodal 4,10-c net with the Schläfli symbol {3(2).4(3).5}{3(4).4(20).5(16).6(5)}. The 2D and 3D coordination networks of 2 and 3, respectively, are characterized by significant overall antiferromagnetic exchange interactions (J/k) between the Co(II) spin centers on the order of -8 and -4 K. The [Mo8O26F2](6-) anion is investigated in detail by quantum chemical calculations.