International Health Act of 1979 - Title I: International Health Subcommittee of the Development Coordination Committee - Amends the Foreign Assistance Act of 1961 to establish the International Health Subcommittee of the Development Coordination Committee which is to develop a comprehensive Federal International Health Plan. Sets forth the duties of the Subcommittee in developing such Plan. Provides for Subcommittee employment and compensation. Title II: Office of International Health - Amends the Public Health Service Act to establish an Office of International Health within the Department of Health, Education, and Welfare to be responsible for international health activities. Directs the Secretary to establish within the Public Health Service: (1) International Health Fellowships; (2) International Health Service; and (3) programs to support international health centers and international health programs in U.S. academic institutions. Title III: The Hubert H. Humphrey Fund - Establishes the Hubert H. Humphrey Fund for International Health as a nonprofit corporation. Sets forth provisions regarding a Board of Directors, officers, and employees. Stipulates that such Fund shall facilitate the improvement in the health status of people in developing countries. Requires the Fund to report annually to the President and Congress concerning its operations.