The dynamics of phase separation of ternary mixtures into two and three phases are analyzed numerically by solving the nonlinear spinodal decomposition equations in two dimensions. We find interesting interface effects during the decomposition process. Between any two alpha + beta phases rich in components I and J respectively, the third component K segregates in the interface between alpha and beta. We study the interface segregation effects in symmetric ternary polymer blends (i.e., with equal Flory interaction parameters between each pair of monomers and equal degrees of polymerization). This segregation phenomenon influences strongly the growth of a third phase with lowest equilibrium volume fraction. In the absence of hydrodynamics, the kinetics of the minority phase is determined by the topology of the segregation pattern initiated by the decomposition of the most unstable phases. Coarsening of the minority phase occurs at the junction of four or more majority phase domain boundaries. We examine the dynamical scaling and the growth laws for the late stages of separation into two and three phases. The growth law R(tau) similar to tau(1/3) is always obeyed even when the structures are not self-similar. The self-similar regime is achieved very slowly in ternary systems.