Ben came from a family of 10 children in Seymour, Iowa. (He was never Bernard except to his mother & sisters). His father was a coal miner who deserted the family; because of this Ben was never proud of the name nor interested in his father's origins. Ben was a football running back in both high school and Des Moines University, whose remnants are now associated with the University of Sioux Falls. He met his future wife, Rhoda Broholm (who was from Denmark), at Des Moines University. Both did graduate work at Berkeley Baptist Divinity School and the University of California. They were both appointed by the American Baptist Foreign Mission Society for service in the Belgian Congo (Zaire) in February 1923. They were married in May, and arrived in the Belgian Congo later that year to serve in Sona Bata.

In 1930 they transferred to a newly opened mission station in Kikongo, where they were involved in both educational and evangelistic work. Dr. and Mrs. Armstrong worked together to improve village life, where there was an enrollment of over 5,000 people in 250 village schools. After furlough in 1941, Dr. and Mrs. Armstrong returned to the Belgian Congo, braving war-time travel to continue their much-needed service.In 1948 Dr. Armstrong was appointed Mission Secretary. His duties included traveling often to eight mission stations where he advised and assisted with conferences. Ben refused to seek or to accept ordination - he didn't have that call, even though he received all appropriate education (mostly at Berkeley). Thus, his being selected field secretary as a layman is a tribute both to his abilities and those of his wife. In 1949 the Belgian government awarded medals to both the Armstrongs for their outstanding contribution to the uplift of the Congolese.Eight years after Rhoda passed away (1958), Ben married Edna Smith, a former Women's American Baptist Foreign Mission Society missionary to South China and Hong Kong. Dr. Armstrong remained in Leopoldville during the uncertain days following the Congo's independence in July, 1960. He presided over the traumatic but ultimately successful transfer of power from Euro-Americans to Congolese national leaders during the Revolution.

In a 1957 newsletter Ben wrote, "Our work is a facet of the missionary job that is almost unknown at home. ... it is not so easy to write inspiringly about the office work. In fact, I have to drive myself even to get most of it done. Still, we know it is necessary. While we are here doing this work, someone better qualified to do the church's work doesn't have to leave that and come here." Ben retired in 1961 and passed away in California in 1981.