A series of nine mixed-ligand metal-organic frameworks (MOFs) have been prepared by the combination of a bent dipyridyl linker 4-amino-3,5-bis(4-pyridyl)-1,2,4-triazole (bpt) and three benzenedicarboxylate isomers (pa = phthalate, ip = isophthalate, and tp = terephthalate), respectively, with different metal ions such as Co-II, Ni-II, Cu-II, Zn-II, and Cd-II. The framework structures of these neutral polymeric complexes have been determined by the X-ray single-crystal diffraction technique. Structural analysis reveals that the benzenedicarboxylate isomers display versatile coordination modes to manage the metal ions to form 1-D chain or ribbon arrays, which are further extended via the exo-bidentate bpt connectors to give rise to a variety of coordination networks, such as a simple (4,4) layer, 2-D double layer with decorated (4,4) topology, 2-D layer with decorated (3,6) topology, 2-D bilayer with 8(2).10 topology (2-fold interpenetration), 3-D polythreaded architecture (1-D + 2-D), and 2-fold interpenetrating porous lattice of (4,4) layers. The accessorial secondary interactions such as hydrogen bonding and/or aromatic stacking are also helpful for the extension and stabilization of the final supramolecular aggregates. This work evidently indicates that the isomeric effect of the anionic benzenedicarboxylate is significant in the construction of these network structures, which are also well regulated by the metal centers. The Zn-II and Cd-II MOFs exhibit strong solid-state luminescence emissions at room temperature, which originate differently from intraligand transition or ligand-to-metal charge transfer. Thermal stability of these crystalline materials has been explored by thermogravimetric analysis of mass loss. The 3-D host frameworks of MOFs 8 and 9 show similar porous cavities, and their desorption/adsorption behaviors of guest solvents have also been investigated.