Can this product be installed between the tar paper and composite shingles

You would not want to do this with our product. The better application would be to get our Radiant Barrier (RB4812550) and apply it to the bottom side of the roof rafters. This product is perforated so it breaths and does not become a vapor barrier causing moisture issues. You would need to install this product leaving around a 6" space at the soffit end, overlap about 2 inches with every sheet moving toward the peak of your roof and leave around a 6" gap at the peak as well. This allows air flow. Do not block off any of your vents or you will have moisture issues from trapping hot air against cold air. When properly installed this product will lower your attic temp. 15-30 degrees. I have this product installed in my home and it works great.

Dear MV: This product and similar reflective / radiant barriers will provide almost zero benefit if they are sandwiched between tar paper and composite shingles. These products offer almost no R-value by themselves; they require a sealed air gap on one side that actually delivers the claimed R-value. An air gap on a roof is clearly not possible. The best option is to insulate the opposite side -- the rafter bays in your attic -- with Roxul ComfortBatt between the rafters. If you live in a region with very hot summers or cold winters, it may also be a good idea to mount 2" of EPS foam board on the bottom of the rafters, carefully air seal all of the joints and edges with DAP 230, and insulate your gable end walls in the same way -- then close all of the vents and create a sealed attic that will become 'conditioned space". Also make sure you seal every air leak into your attic from the floor below. This is almost as important as insulation. All of the products mentioned above are available from Lowes. I hope this is helpful. Mark