The emergence of heterogeneous applications with diverse requirements for resource-constrained Wireless Body Area Networks (WBANs) poses significant challenges for provisioning Quality of Service (QoS) with multi-constraints (delay and reliability) while preserving energy efficiency. To address such challenges, this paper proposes McMAC,a MAC protocol with multi-constrained QoS provisioning for diverse traffic classes in WBANs. McMAC classifies traffic based on their multi-constrained QoS demands and introduces a novel superframe structure based on the "transmit-whenever-appropriate"principle, which allows diverse periods for diverse traffic classes according to their respective QoS requirements. Furthermore, a novel emergency packet handling mechanism is proposedto ensure packet delivery with the least possible delay and the highest reliability. McMAC is also modeled analytically, and extensive simulations were performed to evaluate its performance. The results reveal that McMAC achieves the desired delay and reliability guarantee according to the requirements of a particular traffic class while achieving energy efficiency.