He went to Sydney Boys High School then studied medicine at the University of Sydney, graduating with his brother Henry in 1906. He became resident at Sydney Hospital in 1906, then went to Coolgardie, Western Australia. He married in Perth in 1908 and returned to NSW by 1910 when he set up as a general practitioner at Woonona. In 1915 he enlisted in the Australian Army Medical Corps. He served as a captain in France in 1916 but was invalided home in May 1917 and discharged from the AIF. After working as an army medical officer at Bulli in 1917-18, he resumed general practice and became honorary repatriation medical officer, government medical officer and Commonwealth medical referee for the Bulli district, posts he held until his retirement in 1955.

During the Depression Charles treated many families without charge and later welcomed the national health schemes. He founded branches of the Ladies' Home Nursing Service and women's first aid classes, and was active in many local organisations,, including the NSW Society for Crippled Children, Wollongong High School, Police Boys Club and Presbyterian Church. A surgeon within the St John Ambulance Brigade in 1928-55, he was appointed officer brother in the Order of St John of Jerusalem in 1939. A wing of Bulli District Hospital was named Palmer House.

He died at Bulli in 1955 and was survived by his second wife and their son, and by two sons and two daughters by his first marriage. His estate was sworn at £49,715.