A new dinuclear copper(II) complex bridged by N-[3-(dimethylamino)propyl]-N′- (2-carbo-xylatophenyl)oxamide (H3dmapob), and endcapped with 2,2′-diamino-4,4′-bithiazole (dabt), namely [Cu2(dmapob)(dabt)(CH3OH)(pic)]·(DMF)0.75·(CH3OH)0.25 has been synthesized and characterized by elemental analysis, molar conductivity measurement, infrared and electronic spectra studies, and single-crystal X-ray diffraction. In the crystal structure, both copper(II) ions have square–pyramidal coordination geometries. The Cu···Cu separation through the oxamido bridge is 5.176(9) Å. A two-dimensional supramolecular framework is formed through hydrogen bonds and π–π stacking interactions. The reactivities toward herring sperm DNA and bovine serum albumin (BSA) show that the complex can interact with the DNA via intercalation mode and bind to the BSA responsible for quenching of tryptophan fluorescence by the static quenching mechanism. The in vitro anticancer activities suggest that the copper(II) complex is active against the selected tumor cell lines. The influence of different bridging ligands in dinuclear complexes on the DNA- and BSA-binding properties as well as anticancer activities is preliminarily discussed.