I hope this helps i have just created the intersect manually by using a projected curve and the quick trim tool
Project sketch into a new sketch
Draw a line along the horizontal plane, using the quick trim tool split the projected curve by removing the bottom section first, then split one of the remaining curves with the other. and turn the line you used as the splitting tool into a construction line.
draw a line using the point shown, (this is the interception line)
split the surface with the plane shown, leaving the bottom section of the curve
split the original surface again but leaving the top two sections and then keep all elements and extract both surfaces individually
using the line that was drawn in step 3 split the surface you extracted
finally join all of the requited surfaces
I hope this helps i do not know to do this without manually creating the intersect curve.