The "Healthy Servicemembers Act" mandates the Secretary of Defense to implement a comprehensive program for military personnel and their families affected by unsafe housing. This includes establishing a screening process at military medical treatment facilities for individuals with health conditions linked to their housing, with procedures allowing for inclusion in a registry. The bill requires the creation and maintenance of a registry to track eligible individuals who have developed "covered conditions" from residing in unsafe housing units. The Secretary must also launch a public information campaign to inform potential registrants about the registry's purpose, registration methods, and benefits. An "unsafe housing unit" is defined as one that fails to meet established housing quality standards or contains dangerous levels of mold.