I know many keep their stock AT tires and/or buy new AT tires. Goodyear has come out with a new Wrangler AT that sounds pretty good if they will make one to fit the H2.
The Goodyear Wrangler featuring SilentArmor Technology has 2 high-tensile steel belts and a layer made with Kevlar. It also has the Durawall, that is more puncture resistant, like what the MT/R has. It has some type of rim guard that will keep the wheel edge off of rocks. With the rim guard and durawall, they should air down pretty well for off-road use.
http://www.goodyearwrangler.com/