Co-crystallisation of 1,2-bis(amidino-O-methylurea)ethanecopper(II) tetrafluoroborate [CuL][BF4]2 with cytosine or thymine leads to compounds with 1 ∶ 2 or 1 ∶ 1 molar ratios of [CuL]2+ to DNA pyrimidine base, respectively. As both the DNA bases and the cation, which comprises a copper(II) centre co-ordinated by a tetradentate 1,2-bis(amidino-O-methylurea)ethane ligand, are planar species with considerable hydrogen-bonding potential, both products adopt 2-D sheet architectures. A structural building block common to both compounds comprises a pair of cations linked through pairs of DNA bases by diverse hydrogen-bonded contacts. In the cytosine compound, the building blocks are linked by pairs of DNA bases to form a 1-D linear chain with 1 ∶ 2 [CuL]2+ ∶ cytosine molar ratio; in the thymine compound, the building blocks are linked by pairs of water molecules and tetrafluoroborate anions to generate a 1-D linear chain with 1 ∶ 1 [CuL]2+ ∶ thymine molar ratio. Tetrafluoroborate-mediated hydrogen-bonded assemblies serve to connect the chains into sheets. The stacking of the sheets also involves tetrafluoroborate-mediated hydrogen-bonded assemblies as well as very weak co-ordinate Cu⋯O interactions for the cytosine complex and O–H⋯F water–tetrafluoroborate hydrogen-bonded contacts for the thymine complex.