Try the Drape command. That will give you a NURBS surface that will be much easier to deal with in Rhino than the meshes you've got. Once you've draped it, intersect it with a plane and Split both of them. Even if it won't join together into a solid, it will let you create curves on the surfaces that you can use to reconstruct your geometry and generate new surfaces using Loft, NetworkSrf or another surfacing command. If you construct those correctly, they should join up to form closed polysurfaces.