Fallen Heroes and Families Assistance Act - Amends the Pay Our Military Act (P.L. 113-39) to make FY2014 appropriations, out of any money in the Treasury not otherwise appropriated, for any period during which interim or full-year appropriations for FY2014 are not in effect, for such sums as are necessary to continue programs and activities concerning:

• payment of death gratuities to certain survivors of deceased military service members, including for the death of members on active duty or inactive duty training, the death of members after discharge or release from duty or training, members and employees dying outside the United States while assigned to intelligence duties, and other eligible survivors;
• payment of pay and allowances due a member of the Armed Forces and unpaid at the time of the member's death;
• payment of authorized funeral and burial expenses, including authorized funeral travel and travel related to the dignified transfer of remains and unit memorial services; and
• continuation of a basic allowance of housing for certain dependents of members dying on active duty.