Mental and Physical Health Care Comorbidities Act of 2023 This bill establishes a demonstration program to test hospital innovations that support low-income or uninsured individuals with serious mental and physical health comorbidities and to identify appropriate payment reforms under Medicare and Medicaid. Participating hospitals must (1) have a proportionally high number of Medicare or Medicaid patients, and (2) develop a plan and related quality metrics for innovations to provide coordinated care and address social determinants of health for individuals with serious mental illness or emotional disturbance and physical comorbidities (e.g., chronic conditions).