In　this　article,　we　study　two-phase　fluid　flow　in　coupled　free　flow　and　porous　media　regions.　The　model　consists　of　coupled　Cahn-Hilliard　and　Navier-Stokes　equations　in　the　free　fluid　region　and　the　two-phase　Darcy　law　in　the　porous　medium　region.　We　propose　a　Robin-Robin　domain　decomposition　method　for　the　coupled　Navier-Stokes　and　Darcy　system　with　the　generalized　Beavers-Joseph-Saffman　condition　on　the　interface　between　the　free　flow　and　the　porous　media　regions.　Numerical　examples　are　presented　to　illustrate　the　effectiveness　of　this　method.　(C)　2014　Elsevier　Inc.　All　rights　reserved.