The structure, electronic, spectral, and optical properties of ternary semiconducting materials CuXY2 (X = Sb, Bi; Y= S, Se, Te) are computed by using Density Functional Theory (DFT) technique. The ground state configurations show that these systems have distorted rhomboidal structures in singlet states. It is found that CuSbY2 possesses higher Highest Occupied Molecular Orbital (HOMO) – Lowest Unoccupied Molecular Orbital (LUMO) energy gap than CuBiY2. We have employed three different levels of theories (B3LYP/LANL2DZ, Relativistic Effective – Core Potentials (RECPs) - CRENBL++, LANL08+) to study the electronic states. The energy gaps of these materials vary from 1.926 eV to 2.183 eV and 1.862 eV to 2.340 eV respectively at different levels of theory, suggesting their suitability as solar cell absorbents. The DFT based global structural descriptors are computed and analysed with the help of vertical ionization energy, and vertical electron affinity. The optical properties such as optical electronegativity, refractive index, dielectric constant and IR and Raman activities are studied. Our results show that the optical electronegativity of CuSbY2 is higher than that of CuBiY2 whereas the refractive index of CuSbY2 is smaller than that of CuBiY2. The computed harmonic frequencies, and maximum intensities of IR and Raman spectra decline from S to Se to Te for Systems CuSbY2 and CuBiY2. Our computed electrostatic potentials and other electronic properties show that CuBiY2 systems differ substantially from CuSbY2 because of relativistic effects on Bi.