I am sorry - this is not a solution. I hope someone will come up with a real answer to your problem. This is just an explanation why you do not get it to work in the first place and what other problems there are with Freestyle.
Unfortunately you cannot create what you want with Freestyle, or at least not really in a simple way. The main reasons you'll find in the Blender Documentation on Freestyle's Known Limitations:
So the first thing is, your edge will not work in Freestyle because only faced mesh objects are supported. Now you could extrude the edge to create a face, and if you mark only one edge as Freestyle Edge and use Edge Mark in the Edge Type settings this might have been the way to go...
However, there comes the other limitation: "No edges at face intersections are detected yet" - and what the problem with this is I'll show you with an example. I've set up a thicker line for the visible edges and a thinner dashed line for the hidden edges and have two objects in my scene. Rendered separately, everything looks fine and as expected:
Now when objects are in the more or less same location, they are overlapping each other. The larger object hides a lot of the smaller object, which also hides a bit of the parts lying behind it from the camera's view. What you would expect to see is something like this on the right side:
But unfortunately, since _Freestyle is not very good at detecting which edges are visible and which not when faces are intersecting, the actual result you'll get is this:
So here is what I did with your file, I extruded the edge just a little bit to have a face and marked one of them as Freestyle Edge:
But due to the limitations of Freestyle, the result does not look as if the edge was going through the planes but as if it is completely behind them:
And if I had made the extruded face larger, although only one edge is marked as Freestyle Edge, rendering it now would make it even worse because the face would still work as an obstacle hiding the edges of the planes:
All in the only way I see right now is somehow splitting up the edge in several parts and trying to find ways to make everything visible the way it is supposed to be. But as soon as you would be going for a different camera angle you would have to adjust all again. Or you have to render the parts separately and create the correct visible/hidden segments in another software. The best would be of course someone knew a better way which makes it all work automatically the way you want.