Servicemember Family Burial Act This bill revises eligibility for Department of Veterans Affairs (VA)-provided memorial headstones and markers that commemorate individuals whose remains are unavailable. The bill makes eligible the spouse or eligible dependent child of a member of the U.S. Armed Forces serving on active duty under other than dishonorable conditions at the time of the spouse's or child's death. The spouse, minor child, and, in the VA's discretion, unmarried adult child of such a member of the Armed Forces may be buried in any open national cemetery under the control of the National Cemetery Administration.