We have studied the evolution of microstructure when a disordered ternary alloy is quenched into a ternary miscibility gap. We have used computer simulations based on multicomponent Cahn-Hilliard (CH) equations for cA and cB, the compositions (in mole fraction) of A and B, respectively. In this work, we present our results on the effect of relative interfacial energies on the temporal evolution of morphologies during spinodal phase separation of an alloy with average composition, cA = 1/4, cB = 1/4 and cC = 1/2. Interfacial energies between the 'A' rich, 'B' rich and 'C' rich phases are varied by changing the gradient energy coefficients. The phases associated with a higher interfacial energy are found to be more rounded than those with lower energy. Further, the kinetic paths (i.e. the history of A-rich, B-rich and C-rich regions in the microstructure) are also affected significantly by the relative interfacial energies of the three phases.