Wireless body area networks (WBANs) are a research area that supports patients with healthcare monitoring. In WBAN, the Internet of Things (IoT) is connected with WBAN for a smart/remote healthcare monitoring system in which various medical diseases are diagnosed. Quality of service (QoS), security and energy efficiency achievements are the major issues in the WBAN-IoT environment. Existing schemes for these three issues fail to achieve them since nodes are resource constrained and hence delay and the energy consumption is minimized. In this paper, a blockchain-assisted delay and energy aware healthcare monitoring (B-DEAH) system is presented in the WBAN-IoT environment. Both body sensors and environment sensors are deployed with dual sinks for emergency and periodical packet transmission. Various processes are involved in this paper, and each process is described as follows: Key registration for patients using an extended version of the PRESENT algorithm is proposed. Cluster formation and cluster head selection are implemented using spotted hyena optimizer. Then, cluster-based routing is established using the MOORA algorithm. For data transmission, the patient block agent (PBA) is deployed and authenticated using the four Q curve asymmetric algorithm. In PBA, three entities are used: classifier and queue manager, channel selector and security manager. Each entity is run by a special function, as packets are classified using two stream deep reinforcement learning (TS-DRL) into three classes: emergency, non-emergency and faulty data. Individual packets are put into a separate queue, which is called emergency, periodical and faulty. Each queue is handled using Reyni entropy. Periodical packets are forwarded by a separate channel without any interference using a multi objective based channel selection algorithm. Then, all packets are encrypted and forwarded to the sink nodes. Simulation is conducted using the OMNeT++ network simulator, in which diverse parameters are evaluated and compared with several existing works in terms of network throughput for periodic (41.75 Kbps) and emergency packets (42.5 Kbps); end-to-end delay for periodic (0.036 s) and emergency packets (0.028 s); packet loss rate (1.1%); residual energy in terms of simulation rounds based on periodic (0.039 J) and emergency packets (0.044 J) and in terms of simulation time based on periodic (8.35 J) and emergency packets (8.53 J); success rate for periodic (87.83%) and emergency packets (87.5%); authentication time (3.25 s); and reliability (87.83%).