In this study, a detailed investigation of the electronic and optical properties (i.e., binding energies, absorption wavelength, overlap of the electron-hole wave functions, recombination oscillator strength, etc.) of an exciton and a biexciton in CdTe/CdSe core/shell type-II quantum dot heterostructures has been carried out in the frame of the single band effective mass approximation. In order to determine the electronic properties, we have self-consistently solved the Poisson-Schrodinger equations in the Hartree approximation. We have considered all probable Coulomb interaction effects on both energy levels and also on the corresponding wave functions for both single exciton and biexciton. In addition, we have taken into account the quantum mechanical exchange-correlation effects in the local density approximation between same kinds of particles for biexciton. Also, we have examined the effect of the ligands and dielectric mismatch on the electronic and optical properties. We have used a different approximation proposed by Sahin and Koc [Appl. Phys. Lett. 102, 183103 (2013)] for the recombination oscillator strength of the biexciton for bound and unbound cases. The results obtained have been presented comparatively as a function of the shell thicknesses and probable physical reasons in behind of the results have been discussed in a detail. (C) 2014 AIP Publishing LLC.