Fill surface with guide curves

We are trying to create a surface that fills in a sketch and uses 2 curves to create a domed top. Can anyone tell me how to do it?

Here is a quick sketch of what we are trying to create. The 2 cross sketchs are raised.

I have attached a model of this skeleton. I also attached a STEP file of what we are trying to end up with.

*** Note *** we need it to be a curvature continuous surface.