Rosenblum joined the Associated Press at Newark in 1965. His international career began in 1967, when the Associated Press sent him to cover mercenary wars in Congo. Since then Rosenblum has run Associated Press bureaus in Kinshasa, Lagos, Kuala Lumpur, Jakarta, Singapore, Buenos Aires, and Paris.
From 1979 to 1981 he was editor of the International Herald Tribune but later returned to Associated Press as special correspondent, based in Paris.
Rosenblum left Associated Press in 2004, and in 2008, launched dispatches, a quarterly magazine with co-editor Gary Knight and publisher Doctor Simba Gill. Additionally, Rosenblum is a professor of journalism at the University of Arizona, Tucson, where he teaches International Reporting.