Reactions of the semi-rigid N,N′-bis(3-pyridyl)terephthalamide (L) with divalent metal salts in the presence of dicarboxylic acids afforded [Cd(L)0.5(1,2-BDC)(H2O)]n (1,2-H2BDC = benzene-1,2-dicarboxylic acid), 1, {[Cd(L)1.5(1,3-BDC)(H2O)]·5H2O}n (1,3-H2BDC = benzene-1,3-dicarboxylic acid), 2a, {[Cd(1,3-BDC)(H2O)3]·2H2O}n, 2b, {[Cd(L)0.5(1,4-BDC)(H2O)2]·H2O}n (1,4-H2BDC = benzene-1,4-dicarboxylic acid), 3, and [Cu(L)0.5(5-tert-IPA)]n (5-tert-IPA = 5-tert-butylbenzene-1,3-dicarboxylic acid), 4, which have been structurally characterized by single crystal X-ray diffraction. Complexes 1 and 3 are two-dimensional (2D) layers with the bey and the hcb topologies, and 2a and 2b are one-dimensional (1D) ladder and zigzag chain, respectively, while 4 shows a 3-fold interpenetrated three-dimensional (3D) net with the cds topology. The structures of these coordination polymers containing the semi-rigid L ligands are subject to the donor atom positions and the identity of the dicarboxylate ligands, which are in marked contrast to those obtained from the flexible bis-pyridyl-bis-amide ligands that form self-catenated nets. The luminescence of 1 and 3 and thermal properties of complexes 1, 3, and 4 are also discussed.