  Considered in this paper is a bi-directional model for the propagation of
interfacial capillary-gravity waves in a two-layer system of fluids with rigid
lid condition for the upper layer and lower layer with a much larger or
infinite depth. The system is derived from a reformulation of the Euler
equations for internal waves with nonnegligible surface tension effects in the
interface and the corresponding asymptotic model under the Benjamin-Ono regime.
Another unidirectional model, so-called regularized Benjamin equation,
generalizing the Benjamin equation, is also introduced. Well-posedness of the
new equations and existence of solitary wave solutions are discussed.
