His descendant Samuel Sherburne built the 1766 (and later) house which bears Henry's name today in Portsmouth.
Henry was the older brother of John Sherburne, another New Hampshire pioneer.
Colonel Tobias Lear, George Washington's private secretary, was his great grandson.
Sherburne and his brother John were lineal descendants of the illustrious "Sherburne" (or Shireburn) family of England (their ancestors progressively built Stonyhurst Hall in Lancashire, England but lost it when the elder branch of the family, which remained there, became extinct in 1717).
He married twice; first to the daughter of New Hampshire pioneer Ambrose Gibbons, by whom he had many children who have since spread about the New World.