To cope with the exploding mobile traffic in the fifth generation cellular network, the dense deployment of small cells and cognitive radios are two key technologies that significantly increase the network capacity and improve the spectrum utilization efficiency. Despite the desirable features, small cell cognitive radio networks (SCRNs) also face a higher risk of unauthorized spectrum access, which should not be overlooked. In this paper, we consider a passive monitoring system for SCRNs, which deploys sniffers for wireless traffic capture and network forensics, and study the optimal sniffer channel assignment (SCA) problem to maximize the monitoring performance. Unlike most existing SCA approaches that concentrate on user activity, we highlight the inherent error in wireless data capture (i.e. imperfect monitoring) due to the unreliable nature of wireless propagation, and propose an online-learning based algorithm called OSA (Online Sniffer-channel Assignment). OSA is a type of contextual combinatorial multi-armed bandit learning algorithm, which addresses key challenges in SCRN monitoring including the time- varying spectrum resource, imperfect monitoring, and uncertain network conditions. We theoretically prove that OSA has a sublinear learning regret bound and illustrate via simulations that OSA significantly outperforms benchmark solutions.