Two metal–organic frameworks (MOFs) based on Zn(II)-squarate bridges associated with non-covalent and covalent bonds of dpe ligands, [Zn(dpe)(C4O4)(H2O)2]n (1), and {[Zn(Hdpe)(C4O4)0.5(H2O)3][Zn(C4O4)2(H2O)2]}n (2) (C4O42− (squarate) = dianion of 3,4-dihydroxycyclobut-3-ene-1,2-dione (H2C4O4); dpe = 1,2-bis(4-pyridyl)ethane), have been synthesized and characterized by spectroscopic analysis and single-crystal X-ray diffraction studies. Compound 1 is a two-dimensional (2D) metal–organic framework (MOF), being constructed via the crosslinkage of one-dimensional (1D) [Zn(μ1,3-squarate)] chains and 1D sinusoidal-like [Zn(gauche-dpe)] chains. Compound 2 is a 2D tri-layered composite network composed of one cationic polythreading [Zn(Hdpe)(C4O4)0.5(H2O)3]2+ MOF and two anionic [Zn(C4O4)2(H2O)2]2− MOFs with the penetration of the monoprotonated anti-form Hdpe+ ligands dangling above and below the 2D Zn(II)-(μ1,2,3,4-squarate) layer of cationic [Zn(Hdpe)(C4O4)0.5(H2O)3]2+ MOF into the windows of two 2D Zn(II)-(μ1,3-squarate) layers of anionic [Zn(C4O4)2(H2O)2]2− MOFs. Both of their 2D MOFs in compounds 1 and 2 are then extended to 3D supramolecular architectures via the intermolecular hydrogen bonding interaction among the squarate, protonated dpe ligands and water molecules.