display side of plane in orthographic views as wireframe

I use textured planes as backgrounds and ground planes, but find it difficult to position them or position other objects in relation to them because in a side view the planes become invisible in the editor.

I tried the wireframe display mode, but even then a plane viewed from the side just simply disappears.

Is it possible to display a line for planes in their side view?

You could implement OnDrawGizmos() for the objects, and create a visual representation of the plane that way. (This should cause the plane to be visible regardless of orientation.)