Blockchain technology has brought significant advantages for security and trustworthiness, in particular for Internet of Things (IoT) applications where there are multiple organisations that need to verify data and ensure security of shared smart contracts. Blockchain technology offers security features by means of consensus mechanisms; two key consensus mechanisms are, Proof of Work (PoW) and Practical Byzantine Fault Tolerance (PBFT). While the PoW based mechanism is computationally intensive, due to the puzzle solving, the PBFT consensus mechanism is communication intensive due to the all-to-all messages; thereby, both may result in high energy consumption and, hence, there is a trade-off between the computation and the communication energy costs. In this paper, we propose a hybrid-blockchain (H-chain) framework appropriate for scenarios where multiple organizations exist and where the framework enables private transaction verification and public transaction sharing and audit, according to application needs. In particular, we study the energy consumption of the hybrid consensus mechanisms in H-chain. Moreover, this paper proposes a reward plan to incentivize the blockchain agents so that they make contributions to the H-chain while also considering the energy consumption. While the work is generally applicable to IoT applications, the paper illustrates the framework in a scenario which secures an IoT application connected using a software defined network (SDN). The evaluation results first provide a method to balance the public and private parts of the H-chain deployment according to network conditions, computation capability, verification complexity, among other parameters. The simulation results demonstrate that the reward plan can incentivize the blockchain agents to contribute to the H-chain considering the energy consumption of the hybrid consensus mechanism, this enables the proposed H-chain to achieve optimal social welfare.