Keeping Military Families Together Act of 2023 This bill permanently extends certain Department of Veterans Affairs (VA) burial benefits provided to spouses and dependent children of veterans or active duty servicemembers. Specifically, the bill permanently requires the VA to furnish, upon request, memorial headstones or markers for spouses or dependent children of veterans or servicemembers who were serving on active duty at the time of the spouse’s or child’s death. Additionally, the bill permanently authorizes burial in any open national cemetery under the control of the National Cemetery Administration for a spouse or dependent child of veterans or servicemembers who were serving on active duty at the time of the spouse’s or child’s death.