People used tar paper for over a hundred years before the invention of 'house wrap' like Tyvek and Typar. It was the industry standard for the entire structure. I've used it on many a buildings as a exterior wrap. With proper ventilation you won't need to worry about leaving two sides exposed, as it also serves as a water proof barrier for wood protection and wind protection. It has a rather unpleasant vapor release to it so I'd only use it for exterior applications with staples. This product is also known to attract heat, so you may want to consider putting siding over it in the summer time. Over lap it a few inches as there should be an indicator line to show proper lapping. I am a little concerned you want to leave two sides exposed though for 'air flow'. This almost tells me you may or may not have draft issues. Good luck!.
