  We consider a density-stratified fluid composed of two immiscible layers
separated by a sharp interface. We study the regime of long internal waves
interacting with modulated surface wave packets and describe their resonant
interaction by a system of equations where the internal wave solves a
high-order Benjamin-Ono (BO) equation coupled to a linear Schr\"{o}dinger
equation for the envelope of the free surface. The perturbation methods are
based on the Hamiltonian formulation for the original system of irrotational
Euler's equations as described in Benjamin-Bridges [J. Fluid Mech. 333, 1997]
and Craig-Guyenne-Kalisch [Comm. Pure Appl. Math. 58, 2005]. We also establish
a local wellposedness result for a reduced BO-Schr\"{o}dinger system using an
approach developed by Linares-Ponce-Pilod [J. Diff. Eqs. 250, 2011].
