The transport category airplane was in international airspace cruising at flight level 270 in the vicinity of thunderstorms, when the captain reported he illuminated the cabin fasten seatbelt sign, and ordered the cabin crew to take their seats and remain seated. The airplane then entered an area of continuous moderate turbulence. Fifteen minutes into the turbulence encounter, a passenger, who did not have her seatbelt fastened, sustained serious injury when she struck the ceiling of the airplane, and then the armrest of her seat and the floor. The captain declared a medical emergency, and diverted to the nearest airport. The passenger was hospitalized in excess of 48 hours.