the Rhino SDK does not provide a mechanism for finding intersections between meshes and curves. It only supports meshes with (semi-infinite) rays and meshes with polylines.
Would you be happy with converting your curves to polylines first?
Ok, all the intersection functions in RhinoCommon (which you should use from Grasshopper 0.7 onwards) are located in Rhino.Geometry.Intersect.Intersection
You'll find both MeshRay and MeshPolyline there. I see that MeshPolyline actually takes a PolylineCurve instead of a Polyline. I think this is a bit silly. I'll add an overload for that method that takes Polylines directly.
I saw Mesh|Curve in grasshopper. That means we can find the intersection between nurbs curve and mesh too. How did you do this for grasshopper? Will this method be available in RhinoCommon too?