Relevance ranking and result diversification are two core areas in modern recommender systems. Relevance ranking aims at building a ranked list sorted in decreasing order of item relevance, while result diversification focuses on generating a ranked list of items that covers a broad range of topics. In this paper, we study an online learning setting that aims to recommend a ranked list with $K$ items that maximizes the ranking utility, i.e., a list whose items are relevant and whose topics are diverse. We formulate it as the cascade hybrid bandits (CHB) problem. CHB assumes the cascading user behavior, where a user browses the displayed list from top to bottom, clicks the first attractive item, and stops browsing the rest. We propose a hybrid contextual bandit approach, called CascadeHybrid, for solving this problem. CascadeHybrid models item relevance and topical diversity using two independent functions and simultaneously learns those functions from user click feedback. We conduct experiments to evaluate CascadeHybrid on two real-world recommendation datasets: MovieLens and Yahoo music datasets. Our experimental results show that CascadeHybrid outperforms the baselines. In addition, we prove theoretical guarantees on the $n$-step performance demonstrating the soundness of CascadeHybrid.