Seven new coordination polymers, [Co(3-bpcd)(1,3-BDC)(H2O)3]·H2O (1), [Co(3-bpcd)(1,2-BDC)(H2O)]·H2O (2), [Co3(3-bpcd)(1,2,4-BTC)2(H2O)4]·4H2O (3), [Co(3-bpcd)(NPH)]·2H2O (4), [Cu(3-bpcd)(1,3-BDC)] (5), [Cu(3-bpcd)(1,2-BDC)] (6), [Cu(3-bpcd)(1,3,5-HBTC)(H2O)]2·2H2O (7) (3-bpcd = N,N′-bis(pyridin-3-yl)cyclohexane-1,4-dicarboxamide, 1,3-H2BDC = 1,3-benzenedicarboxylic acid, 1,2-H2BDC = 1,2-benzenedicarboxylic acid, 1,2,4-H3BTC = 1,2,4-benzenetricarboxylic acid, H2NPH = 3-nitrophthalic acid and 1,3,5-H3BTC = 1,3,5-benzenetricarboxylic acid) have been hydrothermally synthesized by assembling transition-metal cobalt–copper salts with semi-rigid bis-pyridyl-bis-amide ligand 3-bpcd and different aromatic polycarboxylic acids. Complex 1 exhibits a one-dimensional (1D) sinusoidal-like chain, which is further assembled into a three-dimensional (3D) supramolecular framework through hydrogen-bonding interactions. Complex 2 possesses a 3D framework with 4-connected 66 topology, which contains a two-dimensional (2D) distorted asymmetric hexagonal grid. When 1,2,4-BTC is used in complex 3, a 3D framework with (63·82·10)2(65·8)2(8) topology is constructed. Complex 4 possesses a 3D framework with 4-connected 66 topology, which is similar to that of 2 except for containing a 2D symmetric hexagonal grid. When CoII ion is replaced by CuII ion, the 3D framework of complex 5 with (4·62)(4·66·83) topology based on 3-bpcd and 1,3-BDC ligands is obtained. Complex 6 shows a 2D cross network consisting of a superposed Cu-3-bpcd 1D chain and 1,2-BDC, which is further expanded into a 3D supramolecular framework by hydrogen-bonding interactions. In complex 7, 1,3,5-HBTC is employed as the auxiliary ligand, and a 3D supramolecular framework based on the undulated 2D layers is formed through π–π stacking and hydrogen-bonding interactions. Both the metal ions and polycarboxylates play important roles in the construction of the title complexes. In addition, the electrochemical behaviors and the fluorescence properties of the seven complexes have been investigated.