Henry R. Dunham was born around 1838 in Pennsylvania to John and Laura Dunham. His father was a carpenter who owned $300 of real estate and $600 of personal property by 1860. The family lived in Laporte, Pennsylvania, and by 1860, Dunham was studying law. On August 28, 1862, he received a commission as a 1st lieutenant in Company K of the 141st Pennsylvania Infantry. He was discharged for disability on December 9, 1862. After leaving the army, he returned to Laporte and began practicing law.
He rejoined the Union army in early 1864, mustering in as a private in Company E of the 186th Pennsylvania Infantry on February 24, 1864. A year later, on January 1, 1865, he became a 2nd lieutenant in Company F of the 30th USCT Infantry. The regiment took part in the Carolinas campaign, and he was promoted to 1st lieutenant on July 28, 1865. He mustered out on December 10, 1865.
Dunham returned to Laporte after the war and resumed his work as a lawyer. He married Fidella Teed in Lewisburg, Pennsylvania, on December 1, 1869. They had two children: Ethelin, born around 1872; and John, born around 1873. They moved to Republican, Kansas, around 1869. He worked as a lawyer and Fidella worked as a school teacher. By 1870, they owned $1,600 of real estate and $200 of personal property. They moved to Grant, Kansas, in the early 1870s, and Dunham worked as a farmer there. He died in Laporte, Pennsylvania, on September 5, 1877, probably while visiting his brother Edwin.