Born in Jericho, New York, he received a bachelor of science from Yale University and attended Harvard Law School before enlisting in the United States Naval Reserve as a Seaman Second Class on 8 November 1940. After serving briefly at Floyd Bennett Field, Brooklyn, New York, Underhill was appointed an aviation cadet and was transferred on 6 February 1941 to the Naval Air Station, Jacksonville, Florida, for flight training. He subsequently underwent further training at Miami, Florida; was designated a naval aviator on 15 July; and was commissioned an ensign in the Naval Reserve on 6 August. Following advanced flight training at Norfolk, Virginia, he reported to Scouting Squadron 5 (VS-5).
In May 1942, when Rear Admiral "Jack" Fletcher's Task Force 17 steamed in the Coral Sea seeking to foil Japan's attempt to extend her influence southward, Underhill was with VS-5 on board carrier USS Yorktown (CV-5). When VS-5 raided Tulagi on the morning of 4 May he flew his Dauntless dive-bomber against a heavy anti-aircraft barrage and contributed to the sinking or damaging of eight enemy vessels.
On the morning of 7 May, a coordinated attack group of 17 SBDs from VS-5 took off from Yorktown and, in clear skies with unlimited visibility, launched a dive bombing attack on the light carrier Shoho. The American planes scored nine direct hits and two near misses that sent the hapless enemy flattop to the bottom.
The next day, the two naval forces at last found one another and the stage was set for the first great naval action between aircraft carriers, the Battle of the Coral Sea. On the morning of 8 May, Yorktown launched the SBDs of VS-5, dividing the group to accomplish separate missions. One division joined in the attack on Japanese carrier Shokaku and, diving from 17,000 feet through broken cloud cover, dropped bombs which bent the enemy carrier's deck sufficiently to prevent the launching of her aircraft. As the bombers pulled out, Japanese fighter planes swarmed out to repel them but were fought off by the Americans.
Later that morning, dive bombers of VS-5 conducted anti-torpedo plane patrol around Yorktown's formation. Pressed into service due to the lack of fighters, the slower Dauntless dive-bombers were at a disadvantage with the Japanese attackers. At 1110, eight of the American bombers intercepted and engaged a group of about 17 Japanese fighter planes, shot down six of the enemy and damaged seven more. When the fierce action was over, Ensign Underhill was numbered among those lost in the fight to protect the carrier.
He was posthumously awarded the Navy Cross for his extraordinary heroism, and became the namesake for the destroyer escort USS Underhill (DE-682).