The secondary users (SUs) in cognitive heterogeneous networks have the capability of utilizing the coexisting multi-radio access (MRA) networks to further improve network capacity as well as user satisfaction. In this paper, we focus on multi-radio resource management for the parallel multi-radio access technology in a cognitive multi-cell, where SUs have different services demands, including real-time (RT) services and best-effort (BE) services. Since the interference introduced to the primary users must be considered carefully in order to forbid their performance degradation, the proposed resource management strategy jointly handles the interference problem and the varied resource constraints caused by MRA networks simultaneously. Additionally, because all the users expect to be allocated a fair amount of resource and gain a same level of QoS, the proportional fairness criterion is introduced and aims at all the SUs. Therefore, the proposed strategy can achieve the fairness between RT SUs and BE SUs when the residual resource is sufficient after satisfying the target rate of the RT SUs. Since the formulated problem is NP-hard, a novel algorithm based on genetic algorithm is addressed to solve it. Finally, extensive simulations are presented to verify the performance improvement of the proposed strategy.