A new binuclear copper(II) Schiff base complex [Cu₂ L₂⁻ (NO₃)₂]·2CH₃OH (1) [L = 2,6-bis((E)-(p-tolylimino)methyl)-4-methoxyphenol] was synthesized using a template method in which the tridentate N₂O Schiff base ligand was derived from [1 + 2] condensation of 2,6-diformyl-4-methoxyphenol and p-methyl aniline in the presence of copper(II) ions as the template agent. The X-ray diffraction analyses revealed that this complex crystallizes in the monoclinic system with space group P2₁/n. The most remarkable structural feature of 1 is that it contains two types of 1D right-handed helical chains. The molecules are linked by intermolecular hydrogen bonds and π⋯π interactions, then a 3D supramolecular network was constructed. Moreover, the intermolecular interactions on the crystal packing of 1 have been further studied using Hirshfeld surface analysis and corresponding 2D fingerprint plots. Binding interaction of this complex with calf thymus DNA (CT-DNA) has been investigated using absorption and emission studies, viscosity experiments and circular dichroism studies. Complex 1 shows significant binding to the DNA. The results of fluorescence spectroscopy and UV absorption spectroscopy, CD spectroscopy and viscosity indicated that this complex interacted with CT-DNA in a groove binding mode where the binding constant was 1.3 ± 0.2 × 10⁴ L mol⁻¹. Our fluorimeteric study showed that the reaction between 1 and CT-DNA was exothermic (ΔH = 59.6 kJ mol⁻¹; ΔS = 268.79 J mol⁻¹ K⁻¹). Antibacterial activities of the complex were screened by the disc diffusion method against three Gram-positive bacteria (Staphylococcus aureus ATCC 25923, Enterococcus faecalis ATCC 23212 and S. epidermidis ATCC 34384), and three Gram-negative bacteria (Escherichia coli ATCC 25922, Pseudomonas aeruginosa ATCC 27853 and Klebsiella pneumonia ATCC 70063). The results indicated that this complex demonstrated acceptable antibacterial activities.