Armstrong met Janet Elizabeth Shearon, who was majoring in home economics, at a party hosted by Alpha Chi Omega. According to the couple, there was no real courtship, and neither could remember the exact circumstances of their engagement. They were married on January 28, 1956, at the Congregational Church in Wilmette, Illinois.
On March 22, 1956, he was in a Boeing B-29 Superfortress, which was to air-drop a Douglas D-558-2 Skyrocket. He sat in the right-hand pilot seat while the left-hand seat commander, Stan Butchart, flew the B-29. As they climbed to 30,000 feet (9 km), the number-four engine stopped and the propeller began windmilling (rotating freely) in the airstream. Hitting the switch that would stop the propeller's spinning, Butchart found it slowed but then started spinning again, this time even faster than the others; if it spun too fast, it would break apart. Their aircraft needed to hold an airspeed of 210 mph (338 km/h) to launch its Skyrocket payload, and the B-29 could not land with the Skyrocket attached to its belly. Armstrong and Butchart brought the aircraft into a nose-down attitude to increase speed, then launched the Skyrocket. At the instant of launch, the number-four engine propeller disintegrated. Pieces of it damaged the number-three engine and hit the number-two engine. Butchart and Armstrong were forced to shut down the damaged number-three engine, along with the number-one engine, due to the torque it created. They made a slow, circling descent from 30,000 ft (9 km) using only the number-two engine, and landed safely.
Monroe and Miller were married in a civil ceremony at the Westchester County Court in White Plains, New York, on June 29, and two days later had a Jewish ceremony at the Waccabuc, New York home of Kay Brown, who was Miller's literary agent.
Having become one of Hollywood's most popular box-office attractions, she starred in a series of successful films during the remainder of the decade, including her BAFTA- and Golden Globe-nominated role as Natasha Rostova in War and Peace (1956), an adaptation of the Tolstoy novel set during the Napoleonic wars, starring Henry Fonda and her husband Mel Ferrer.
On 7 November 1956, the first UN peacekeeping force was established to end the Suez Crisis; however, the UN was unable to intervene against the USSR's simultaneous invasion of Hungary following that country's revolution.