The certified flight instructor was giving instruction to a commercial rated pilot in a single-engine experimental airplane that the commercial pilot had never flown before. On the second landing, the commercial pilot failed to lower the nose wheel in a timely manner onto the ground and the airplane became airborne. The airplane veered to the right in a 20 degree bank before the instructor was able to take the controls and level the wings. The airplane touched down a second time and traveled off the runway in the dirt before the nose gear separated and the airplane struck a berm. The commercial pilot reported that there were no mechanical deficiencies with the airplane or engine.