  Using the relativistic equations of radiation hydrodynamics in the viscous
limit, we analyze the boundary layers that develop between radiation-dominated
jets and their environments. In this paper we present the solution for the
self-similar, 2-D, plane-parallel two-stream problem, wherein the jet and the
ambient medium are considered to be separate, interacting fluids, and we
compare our results to those of previous authors. (In a companion paper we
investigate an alternative scenario, known as the free-streaming jet model.)
Consistent with past findings, we show that the boundary layer that develops
between the jet and its surroundings creates a region of low-density material.
These models may be applicable to sources such as super-Eddington tidal
disruption events and long gamma-ray bursts.
