Many real systems are represented in form of multiplex networks composed of a set of nodes, multiple layers of links, and coupling node relationships across all layers. These systems are very vulnerable to damages during both attacks and recoveries due to potential node cascading failures (NCFs). Although some progress has recently been made in studying network robustness and resilience, the comprehensive impacts of coupling node relationships and community structures on NCFs remain unclear. Accordingly, in this article, we study the robustness and resilience of multiplex networks in the presence of NCFs caused by coupling node relationships and community structures. We first model the failure processes of multiplex networks during both attacks and recoveries as node-community cascading failures (called NCCFs), and then theoretically demonstrate the fragility of multiplex networks to random node damages under NCCFs. Subsequently, to improve network robustness and resilience, we adopt a node protection strategy and propose a cost-aware constrained optimization problem. Finally, we devise a degree-based simulated annealing algorithm for solving this optimization problem. Extensive experiments on both simulated and real multiplex networks show that NCCFs make networks more vulnerable to unpredictable damage than classical NCFs. The results also show the superiority of the proposed algorithm over the state-of-the-art algorithms in improving network robustness and resilience.