Instead, use two webcams and two projects pointed at two whiteboards to synchronize the content on both boards.
At it's most basic, you could simply project the video feed from the other camera onto your whiteboard. But, if you want to get fancy, you could use OCR to digitize the planning session and synchronize it to a To Do manager like Asana.com. Then, instead of seeing the other person's back, you'd see a digitized list of their To Do items. You could even cross them out, or add items of your own, and it would sync to the other person's whiteboard!
How would you improve this idea? Let us know! And, of course, if you go ahead an make it, we’d love to see it!