Strengthening Tribal Families Act of 2023 This bill establishes requirements related to state compliance with the Indian Child Welfare Act of 1978 (ICWA). The ICWA establishes minimum federal standards for the removal of Indian children from their families and the placement of these children in foster or adoptive homes. Specifically, the bill requires a state plan for child welfare services and a state plan related to the Promoting Safe and Stable Families Program to ensure that the agency administering or supervising the plan (e.g., a child welfare agency) shall comply with all federal standards established under the ICWA. Further, the Department of Health and Human Services (HHS) and the Department of the Interior must, in consultation with Indian tribal organizations and states, develop a memorandum of understanding that specifies the factors for measuring compliance with the ICWA. These factors must include requirements sufficient to assess state strengths and areas for improvement in implementing the ICWA (e.g., timely tribal notice of state child custody proceedings). Additionally, the bill directs HHS to submit biennial reports to Congress on certain reviews of child and family service programs.