To investigate the effect of organic anions on the coordination frameworks, we synthesized three new complexes, namely, Co(SDBA)(BIMB) (1), Co2(SA)(BIMB)1.5(H2O) (2) and Co(FBA)(BIMB)0.5·H2O (3) (H2SDBA = 4,4′-dicarboxybiphenylsulfone, H4SA = 3,3′,4,4′-diphenylsulfonetetracarboxylate acid and H2FBA = 4,4′-(hexafluoroisopropylidene)bis(benzoic acid)), which were obtained by the reactions of 4,4′-bis(1-imidazolyl)biphenyl (BIMB), and three V-shaped aromatic polycarboxylates as organic anions with Co(NO3)2·6H2O. Single crystal structure analysis shows that complex 1 features a 3-fold interpenetrating three-dimensional (3D) framework with CdSO4-type topology. Complex 2 has a previously unknown 3D trinodal (4,4,6)-connected framework with a Schläfli symbol of (4·64·8)2(43·63)2(44·610·8). Complex 3 exhibits a three-dimensional 2-fold interpenetrating pillared helical-layer open framework of α-Po topology based upon binuclear paddlewheel units. The results reveal that the carboxylic building blocks with different conformations play a significant role in promoting the diversity of the observed structural motifs. The magnetic properties of the three complexes as well as the SHG and ferroelectric properties for 1 have also been investigated. Finally, theoretical calculations were carried out on the conformation of the BIMB ligand in the three complexes.