The coordination polymers [Cd-2(bbmb)(2)(L-1)(HL1)(0.5)(H2O)](n) (1), [Cd-2(bbmb)(2)(L-2)(2)(H2O)center dot(H2O)](n) (2), and [Ni(bbmb)(2)(L-3)](n) (3), were synthesized by the hydrothermal reaction of 4,4'-bis(benzimidazol-1-ylmethyl)biphenyl (bbmb) with Cd-II/Ni-II ions in the presence of three flexible aliphatic acids [tricarballylic acid (H3L1), succinate (H2L2), and adipate (H2L3)]. Complexes 1-3 were structurally characterized by elemental analysis, IR spectroscopy and single-crystal and X-ray powder diffraction analyses. Complex 1 presents a 3D 3-nodal (3,4,4)-connected net with 3,4,4T78 topology, 2 exhibits a 3D network with 6(6)-dia topology, whereas 3 is a chain structure and further extended by hydrogen bonding interactions to form a 2D supramolecular network. Structural diversity of these complexes indicates that these frameworks could be tuned by the conformation of bbmb ligand and the different coordination modes of the aliphatic carboxylate co-ligands. The thermal and fluorescence properties, the catalytic activities of complexes 1-3 in a Fenton-like process were investigated.