The Cahn-Hilliard-Cook (CHC) theory for ternary blends composed of an A-B random copolymer (A-r-B), an A homopolymer, and a B homopolymer is presented to investigate the dynamics of early-stage spinodal decomposition (SD). The cases for both fast theory and slow theory have been formulated. The time dependence of the structure factor of a ternary mixture is explored in the case when the mixture is quenched into both three-phase and two-phase regions. The time dependence of the structure factors of homopolymers A and B in the ternary blend is similar to those of binary homopolymer blends composed of A and B. The characteristic parameters of early-stage spinodal decomposition are formulated.