Family Health Care Accessibility Act of 2010

Family Health Care Accessibility Act of 2010 - Amends the Public Health Service Act to deem a health professional volunteer providing primary health care to an individual at a community health center to be an employee of the Public Health Service for purposes of any civil action that may arise from providing services to patients. Sets forth conditions for such liability protection, including: (1) the service is provided to the individual at a community health center or through offsite programs or events carried out by such center; (2) the provider is sponsored by the community health center; (3) the health care practitioner does not receive any compensation for providing the service, except repayment for reasonable expenses; (4) before the service is provided, the health care practitioner or the center posts a clear and conspicuous notice at the site where the service is provided of the extent to which the legal liability of the health care practitioner is limited pursuant to this Act; (5) at the time the service is provided, the health care practitioner is licensed or certified in accordance with applicable law regarding the provision of the service; and (6) the Secretary of Health and Human Services (HHS) transfers funds to an account to cover costs for such coverage.

Considers an entity as sponsoring the health care practitioner if: (1) the entity submits an application to the Secretary; and (2) the Secretary determines that the health care practitioner is deemed to be an employee of the Public Health Service.

Requires the Attorney General to submit to Congress a report providing an estimate of the amount of claims (together with related fees and expenses of witnesses) that, by reason of the actions or omissions of health professional volunteers, will be paid pursuant to this Act during the calendar year that begins in the following fiscal year. Requires the Secretary to transfer such estimated amount from the claims fund to the appropriate accounts in the Treasury, subject to the extent of amounts in the fund.

Makes this Act effective on October 1, 2011, except permits upon its enactment: (1) the Secretary to issue regulations for carrying out this Act and to accept and consider applications under this Act; and (2) the Attorney General to submit reports to Congress under this Act.