A couple of heteroleptic copper(II) complexes, [Cu(HL1)(bpy)](NO3)2.2H2O (4 a) and [Cu (HL1)(phen)](NO3)2.2H2O (4 b), where HL1 is 2-((benzo[d]thiazol-2-ylimino)methyl) phenol, bpy=2,2′-bipyridyl and phen is 1,10-phenanthroline have been synthesized and characterized by elemental analysis, UV/Vis, FTIR, NMR spectroscopic and mass spectrometric techniques. The binding interaction of metal complexes with ct-DNA was assessed by electronic absorption, fluorescence spectroscopy and docking studies. The studies reveal that the complexes 4 a and 4 b interact with DNA via intercalation mode of binding with an intrinsic binding constant (Kb) 1.45 ± 0.21 × 104 M−1 and 4.65 ± 0.21 × 104 M−1, respectively. Further, protein (Bovine serum albumin i. e. BSA) interaction studies revealed the quenching constants (Kb) to be 5.62 × 105 M−1 for complex 4 a and 1.03 × 106 M−1 for complex 4 b. All the spectral data proved about metal complexes bind with ct-DNA and BSA having significant binding affinities. Circular dichroism studies also revels the intercalative mode with conformational changes of ct-DNA with increasing concentrations. DNA binding property of such molecules serves as shape selective conformational probes. Similar compounds are reported to have potential applications in medicinal and diagnostic industries. They have significant roles in the development of fluorescent probes for biological applications. © 2020 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim