Public m-health service will enable care-givers to continuously monitor patients' vital signals wherever they are, using Body Area Networks (BANs). To make this service available to a large number of people everywhere, public m-health service should be implemented in a license-free frequency band. However, the coexistence problem inherent in such a medium that may be shared by many co-located systems may cause disruption of BAN transmissions. This paper addresses the above problem by proposing a Centralized BAN Access Scheme (CBAS) to improve service availability and robustness of BANs. CBAS puts most of the complexities in the gateway, which has less energy and resource constraints than the body nodes. The gateway monitors all the available channels and assigns an interference-free channel to each scheduled node. Extensive simulation results show the effectiveness of CBAS in reducing durations of service interruption and thus improving service reliability of a BAN.