His mother was the granddaughter of Mateo de Toro Zambrano, 1st Count of La Conquista.
Five of his siblings lived to adulthood.
His father committed suicide in 1891, when Enrique was 13 years old.Balmaceda started his political career by joining the Liberal Democratic Party and was promptly elected deputy for "Itata" (1906–1909) in a 1907 by-election to replace deputy Alberto Sanfuentes who had died, but lost his bid for reelection.
In the congressional elections of 1918, he was elected deputy for "Castro" (1918–1921) and was reelected for the same region (1921–1924).
On 12 May 1921, President Arturo Alessandri appointed him Minister of War and Navy, position he held until 16 August 1921.During the first administration of President Carlos Ibáñez he was appointed Minister of the Interior from 23 May 1927 to 24 February 1928; he concurrently served as interim Minister of Public Works and of Justice.
During the second administration of President Ibáñez, he was appointed Ambassador to the United Kingdom.
Balmaceda died in Santiago, in 1962, two months shy of his 84th birthday.