Adaptive mesh refinement (AMR) is a key technology for large-scale simulations that allows for adaptively changing the simulation mesh resolution, resulting in significant computational and storage savings. However, visualizing such AMR data poses a significant challenge due to the difficulties introduced by the hierarchical representation when reconstructing continuous field values. In this paper, we detail a comprehensive solution for interactive isosurface rendering of block-structured AMR data. We contribute a novel reconstruction strategy-the octant method-which is continuous, adaptive and simple to implement. Furthermore, we present a generally applicable hybrid implicit isosurface ray-tracing method, which provides better rendering quality and performance than the built-in sampling-based approach in OSPRay. Finally, we integrate our octant method and hybrid isosurface geometry into OSPRay as a module, providing the ability to create high-quality interactive visualizations combining volume and isosurface representations of BS-AMR data. We evaluate the rendering performance, memory consumption and quality of our method on two gigascale block-structured AMR datasets.