In this work, phase-field models for partially-miscible binary and ternary systems are presented based on the Cahn-Hilliard theory. A binary system is first studied by employing specific free energy function combining two smooth functions which have double-well and single-well structures, respectively. The binary model is then extended to a ternary model. In this case, particular attention is payed to satisfy algebraical and dynamical consistency with the binary system. Finally some numerical results will be presented which demonstrates usefulness of the present model.