Henry was born in Dublin, performed there and in London, and went to Jamaica with Charles Storer and his family about 1762.

He made his New York debut at the opening of the John Street Theatre on December 7, 1767, playing the role of Aimwell in The Beaux' Stratagem.

He left the company in 1794 after disagreements with actor John Hodgkinson, who he had brought to the United States in 1792 together with his wife stage actress Frances Brett Hogkinson.

The first wife, Jane, and their two young children, died at sea during a ship fire in 1767 off the coast of Newport, Rhode Island.

Henry eventually married younger sister Maria, who died shortly after the death of her husband from her grief over his loss.