  We are concerned here with an exact solution to the governing equations for
geophysical fluid dynamics in spherical coordinates which incorporates
discontinuous fluid stratification. This solution represents a steady,
purely--azimuthal equatorial flow with an associated free-surface and an
interface separating two fluid regions, each of which having its own continuous
distribution of density. However, the two density functions do not match along
the interface. Following the derivation of the solution we demonstrate that
there is a well-defined relationship between the imposed pressure at the
free-surface and the resulting distortion of the surface's shape. Moreover,
imposing the continuity of the pressure along the interface generates an
equation that describes (implicitly) the shape of the interface. Interestingly,
it turns out that the interface defining function has infinite regularity.
