Operation Hero Miles Act of 2004 - Authorizes the Secretary of Defense to accept the donation of frequent traveler miles, credits, and tickets for air or surface transportation to facilitate the travel of: (1) a member of the Armed Forces who is deployed on active duty away from his or her permanent duty station and granted leave during such deployment; or (2) family members of such member to be reunited with the member.
Directs the Secretary to reimburse members who participated in the Department of Defense Rest and Recuperation Leave program during the period beginning on September 15, 2003, and ending on December 18, 2003, for travel expenses incurred by the member (or family members on behalf of the member) to travel to or from a designated embarkation point before the program was expanded to include a domestic travel component.