  This paper is concerned with the 2-dim two-phase interface Euler equation
linearized at a pair of monotone shear flows in both fluids. We extend the
Howard's Semicircle Theorem and study the eigenvalue distribution of the
linearized Euler system. Under certain conditions, there are exactly two
eigenvalues for each fixed wave number $k\in \mathbb{R}$ in the whole complex
plane. We provide sufficient conditions for spectral instability arising from
some boundary values of the shear flow velocity. A typical mode is the
ocean-air system in which the density ratio of the fluids is sufficiently
small. We give a complete picture of eigenvalue distribution for a certain
class of shear flows in the ocean-air system.
