In this paper, we study a hybrid interweave-underlay spectrum access system that integrates amplify-and-forward relaying. In hybrid spectrum access, the secondary users flexibly switch between interweave and underlay schemes based on the state of the primary users. A continuous-time Markov chain is proposed to model and analyze the spectrum access mechanism of this hybrid cognitive cooperative radio network (CCRN). Utilizing the proposed Markov model, steady-state probabilities of spectrum access for the hybrid CCRN are derived. Furthermore, we assess performance in terms of outage probability, symbol error rate (SER), and outage capacity of this CCRN for Nakagami-m fading with integer values of fading severity parameter m. Numerical results are provided showing the effect of network parameters on the secondary network performance such as the primary arrival rate, the distances from the secondary transmitters to the primary receiver, the interference power threshold of the primary receiver in underlay mode, and the average transmit signal-to-noise ratio of the secondary network in interweave mode. To show the performance improvement of the CCRN, comparisons for outage probability, SER, and capacity between the conventional underlay scheme and the hybrid scheme are presented. The numerical results show that the hybrid approach outperforms the conventional underlay spectrum access.