Four copper(II) supramolecular complexes, {[Cu(Hpb)(mal)]·H2O}n (1), (Hpb = 2-(2-pyridyl)-benzimidazole, mal = maleate), [Cu4(pb)4(cro)4(MeOH)2]·2MeOH (2) (cro = crotonate), [Cu2(pb)(Hpb)(mac)3(MeOH)] (3) (mac = α-methacrylate) and [Cu(Hpb)(acr)2(H2O)] (4) (acr = acrylate), based on carboxylate copper(II)-aromatic ligand systems which are assembled by combination of metal coordination, hydrogen-bond and π-π interactions, have been rationally designed and synthesized. Complex 1 forms a 3D supramolecular network with open channels by extending 2D undulating sheets constructed from 1D helical chains. Complex 2 generates a 2D grid-like sheet via unusual finite-chain tetranuclear molecules, with four copper atoms arranged in a line; the unit does not extend further due to the capping effect of the terminal methanol. Complexes 3 and 4 present a 1D sinusoidal structure and a 3D columnar network with 1D ladder-shaped double chains, respectively. Interestingly, coligand Hpb, deprotonated or/and neutral in different supramolecular complexes, provides hydrogen bonding and π-π stacking interactions. In complexes 2, 3 and 4, carboxylate anions show various bridging modes, which are reflected in their magnetic properties. Weak ferromagnetic coupling (syn-anti µ-OCO) exists in 1, antiferromagnetic (syn-syn µ-OCO) and weak ferromagnetic coupling (µ-O of the -COO group) in 2 and antiferromagnetic coupling (syn-syn µ-OCO) in 3.