A series of four new copper(II) heteroleptic complexes, [Cu(2‴-pytpy) (L)] (NO3)2·2H2O (1-4), where 2‴-pytpy=4'-(2'''-Pyridyl)-2, 2':6', 2''-terpyridine, L=bipyridyl (bpy), 1, 10 phenanthroline(phen), dipyridoquinoxaline(dpq) and dipyridophenazine (dppz) were synthesized and characterized by spectroscopic techniques. Further, the molecular structure of the complex (2) was confirmed by single crystal X-ray diffraction technique and the data revealed a penta coordinated, distorted square-pyramidal geometry with triclinic system. The interactions of four complexes with calf thymus DNA and bovine serum albumin (BSA) were investigated by electronic absorption, fluorescence and circular dichroism spectroscopy techniques. Spectral studies substantiated an intercalative binding mode of metal complexes with ct-DNA. Significant binding interactions of the complexes with protein have been further revealed from fluorescence studies. Furthermore, all the four complexes show potential cytotoxicity towards the human liver carcinoma cell line (HepG-2).