A pneumatic tire with a double layer innerliner structure bonded to an inner face of the tire carcass for reducing noise generated by air vibrations inside of the tire's air chamber, and a method of making the tire. The double layer structure includes a first innerliner layer of non-foamed rubber adjacent the carcass and a second innerliner layer of foamed porous rubber forming an innermost surface of the tire. The foamed porous rubber is formed by curing a rubber composition having a nitrogen-releasing foaming agent dispersed therein that decomposes at the vulcanization temperature to release nitrogen gas. The second innerliner layer further has an open-celled structure with a plurality of open cavities that are formed by physically altering the innermost surface of the foamed innerliner layer.