According to Plowdon Stevens, Henry was born at Stonington, Connecticut, on 20 November 1681 and baptized in the Congregational Church there on 18 February 1693. The 2009 Gallup Genealogy states that he was baptized at Stonington (New London County), Connecticut on 18 February 1691/2 (modern-style date is 18 February 1692).
He settled in Plainfield, Connecticut, and was married to Elizabeth Fellows in Plainfield on 2 March 1708/9. By 1715 he had returned to Stonington. On 5 February 1721/2 he was one of the inhabitants of the North Society of Stonington who obtained permission from the Governor and Council of Connecticut to build their Meeting House at the Gravel Nole. His wife Elizabeth was admitted to the North Stonington Church on 16 June 1741. 
Henry died after 16 January 1749/50, when he gave a deed of land to his daughter Elizabeth Stewart.
Children of Henry and Elizabeth (Fellows) Stephens were:
Henry, born at Plainfield, Connecticut on 18 December 1709; married November 10 1731 to Sarah Babcock
Simeon, married 3 November 1737 to Mercy Cotts or Coates
Mary, married 25 August 1736 to John Meeks
Jedediah, baptized 12 August 1716 in the Congregational Church of Stonington; married 4 April 1743 to Mary Rathbone
Lucy born in 1717; married Ephraim Smith 3 January 1744
Elizabeth, married first husband William Stewart, Jr., on 4 December 1740; married second husband Joseph Palmer
Thankful, born 15 January 1725, baptized July 11 1725, admitted to church in the North Society on 16 June 1741; married first husband James Partridge on 24 December 1744; married on 13 October 1773 to second husband Zebulon Stevens
It may be possible to confirm family relationships with Henry by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
However, there are no known yDNA test-takers in his direct paternal line.
Mitochondrial DNA test-takers in the direct maternal line: