In this paper, we investigate users’ performance under the hybrid spectrum access model in the massive cognitive radio network (CRN), where multiple primary users (PUs) and secondary users (SUs) transmit on the same channel simultaneously. SUs first detect the state of the channel via channel sensing and select an appropriate channel access scheme (either underlay or overlay) for their transmissions based on the outcome of the channel sensing. When at least one PU is active, SUs transmit under the underlay channel access scheme by employing the power control technique to ensure that the interference generated in the primary network is below the pre-defined interference threshold. In the absence of PU, SUs transmit with full transmit power under the overlay channel access scheme, thereby maximizing their throughput. Using the tool of stochastic geometry, we obtained tractable analyses for important metrics such as success probability, throughput, and the average age of information (AoI) in both primary and secondary networks, while capturing the interference between the two networks. The obtained analyses offer an efficient way to understand the metrics of AoI, throughput and success probability in the hybrid spectrum access-based CRN. We further compared users’ performance under the hybrid spectrum access scheme with performances under overlay and underlay spectrum access schemes. The outcome of the numerical simulations shows that the hybrid spectrum access scheme can significantly improve the performance of users in the network, while also capturing more key features of real-life systems.