Improving Communications Interoperability Grant Program Act - Amends the Homeland Security Act of 2002 to direct the Secretary of Homeland Security, through the Director of the Office of Grants and Training, to establish the Improve Communications for Emergency Response Grant Program to make grants to states and regions for initiatives to improve interoperable emergency communications for first responders for domestic preparedness and the collective response to natural disasters, acts of terrorism, and other man-made disasters, including initiatives to achieve solutions to statewide, regional, national, and international interoperability.