  We study transmission problems with free interfaces from one random medium to
another. Solutions are required to solve distinct partial differential
equations, $\mbox{L}_{+}$ and $\mbox{L}_{-}$, within their positive and
negative sets respectively. A corresponding flux balance from one phase to
another is also imposed. We establish existence and $L^{\infty}$ bounds of
solutions. We also prove that variational solutions are non-degenerate and
develop the regularity theory for solutions of such free boundary problems.
