From April to May 1862 Greene continued to serve as executive officer on "Monitor" during the Battle of Drewry's Bluff on the James River, Virginia, and later provided naval support for General McClellan's forces on land along that river. Greene was aboard the ship when it foundered in a gale 20 miles off Cape Hatteras on December 31 – January 1, 1863, which Greene survived after being pulled into a lifeboat by the ship's surgeon, Dr. Grenville M. Weeks.