Military Housing Oversight, Maintenance, and Enhancement for Servicemembers Act or the Military HOMES Act This bill (1) requires mold mitigation measures for military families who are residing in military housing, (2) makes publicly available the criteria and metrics to be used by the Department of Defense (DOD) to analyze the performance of landlords that receive incentive fees, (3) establishes a working group to promulgate guidance regarding best practices for mold mitigation in privatized military housing and for determining when the presence of mold in such housing is an emergency situation requiring the relocation of the residents, (4) expands the uniform code of basic housing standards for privatized military housing to include government owned and controlled military family housing inside or outside the United States, (5) appoints at least one Exceptional Family Member Program housing liaison for each military department to assist military families, and (6) requires a report on the progress made by DOD in implementing the recommendations contained in a specified certain Government Accountability Office report regarding military housing.