Ensuring Safe Housing for Our Military Act This bill addresses certain health, safety, and environmental hazards in private military housing units and offers certain protections to service members. Among other things, the bill (1) requires uniform credentials for housing inspectors; (2) allows the Department of Defense (DOD) to withhold payment to landlords over health, safety, or environmental hazard concerns; (3) requires a landlord to pay certain relocation costs in connection with a hazard and to reimburse a tenant for personal property damage; and (4) disallows deposits and certain fees or penalties. DOD must maintain an electronic work order system to facilitate repairs to units.