The two isomorphous title structures, formulated as {[Co(C(10)H(4)O(8))(C(12)H(10)N(2))(H(2)O)(2)].C(12)H(10)N(2)}(n), (I), and {[Co(C(10)H(4)O(8))(C(12)H(12)N(2))(H(2)O)(2)].C(12)H(12)N(2)}(n), (II), respectively, are reported. They crystallize in the space group P\overline{1} with only one formula unit in the asymmetric unit, so that the organic ligands lie about inversion centres and the Co atom lies on an inversion centre. The Co atoms are octahedrally coordinated by a carboxylate O atom from 2,5-dicarboxybenzene-1,4-dicarboxylate (H(2)btc), one N atom from 1,2-di-4-pyridylethene (L) in (I) or from 1,2-di-4-pyridylethane (L) in (II), and one coordinated water molecule, plus their inversion-related species. This particular coordination results in a two-dimensional array, with an elemental unit in the shape of a parallelogram having the Co(II) cations at the corners, linked in one direction by L bridges and in the opposite direction by H(2)btc groups. The L solvent molecules act as pillars between parallel planes, linking them by strong hydrogen bonds where the H atoms lie midway between the formal donor/acceptor atoms in a ;shared' mode. Comparison is made with structures presenting the same structural motif, strongly suggesting that the two-dimensional arrangement reported here might be a very stable robust building block for molecular engineering purposes.