Better Mental Health Care for Americans Act This bill modifies programs and payment rates for behavioral health services under Medicare, Medicare Advantage, the Medicare prescription drug benefit, Medicaid, and the Children's Health Insurance Program (CHIP). For example, the bill provides for specialized payment under the Medicare physician fee schedule of certain mental health and substance use disorder services that are integrated into primary care practice, such as preventive screenings and telehealth treatment. It also establishes and provides funds for a Medicaid demonstration program to provide such services to children in a variety of settings, including schools and hospitals. The bill also requires Medicare Advantage and Medicare prescription drug benefit plans to offer mental health and substance use disorder benefits in a manner that is no more restrictive than other benefits with respect to financial and treatment requirements (i.e., parity in benefits). Additionally, the Centers for Medicare & Medicaid Services must audit state Medicaid and CHIP programs with respect to parity requirements and post its related enforcement actions on its website; the bill provides funds for these purposes.