Henry Foster was born in Sturbridge, Massachusetts, on March 31, 1737, the son of Edward Foster (1714-1775) and Rachel Foster (d. 1803). He served in a provincial regiment at Lake George, New York, during the French and Indian War. He and his wife, Abigail Alexander, were married in Winchester, New Hampshire, and had seven children: Henry (1779-1859), Hannah (b. 1763), Abigail (b. 1766), Rachel (1776-1807), Edward (b. 1778), Moses (b. 1781), and Elisha (b. 1783). Henry Foster died in 1782.
The younger Henry Foster married Polly Hubbard (1785-1870), the daughter of Abner Hubbard (1750-1834) and Esther Hamlin (1760-1836) of Middletown, Connecticut. Abner Hubbard served as sergeant major of the 3rd Connecticut Regiment during the Revolutionary War, and later lived in Norwich, Vermont.