Asham was drafted 71st overall by the Montreal Canadiens in the 1996 NHL Entry Draft and made his NHL debut with Montreal during the 1998–99 season. After parts of four seasons with Montreal, he was traded to the New York Islanders on June 22, 2002, along with a 2002 5th round draft pick for Mariusz Czerkawski. After years of going back and forth between the Canadiens and their American Hockey League affiliate, Asham became a mainstay in the Islanders line-up with his most productive offensive season to date coming during his first season with his new team in 2002–03, when he scored 15 goals and 19 assists for 34 points in 78 games. After four seasons with the Islanders, Asham signed a one-year contract with the New Jersey Devils on August 7, 2007.