Military and Federal Civilian Employee Pay Act - Makes continuing appropriations for FY2014 to provide the pay and allowances of: (1) federal employees, (2) members of the reserve components of the Armed Services who perform inactive duty training during such period, and (3) the commissioned corps of the Public Health Service and the National Oceanic and Atmospheric Administration (NOAA). Provides for payment of the pay and allowances of those employees who were furloughed due to a lapse in appropriations that began on or about October 1, 2013, for the period of such lapse in appropriations.