  We present a large-amplitude existence theory for two-dimensional solitary
waves propagating through a two layer body of water. The domain of the fluid is
bounded below by an impermeable flat ocean floor and above by a free boundary
at constant pressure. For any piecewise smooth upstream density distribution
and laminar background current, we construct a global curve of solutions. This
curve bifurcates from the background current and, following along the curve, we
find waves that are arbitrarily close to having horizontal stagnation points.
  The small-amplitude waves are constructed using a center manifold reduction
technique. The large-amplitude theory is obtained through analytical global
bifurcation together with refined qualitative properties of the waves.
