Point cloud denoising is a fundamental and challenging problem in geometry processing. Existing methods typically involve direct denoising of noisy input or filtering raw normals followed by point position updates. Recognizing the crucial relationship between point cloud denoising and normal filtering, we re-examine this problem from a multitask perspective and propose an end-to-end network called PCDNF for joint normal filtering-based point cloud denoising. We introduce an auxiliary normal filtering task to enhance the network's ability to remove noise while preserving geometric features more accurately. Our network incorporates two novel modules. First, we design a shape-aware selector to improve noise removal performance by constructing latent tangent space representations for specific points, taking into account learned point and normal features as well as geometric priors. Second, we develop a feature refinement module to fuse point and normal features, capitalizing on the strengths of point features in describing geometric details and normal features in representing geometric structures, such as sharp edges and corners. This combination overcomes the limitations of each feature type and better recovers geometric information. Extensive evaluations, comparisons, and ablation studies demonstrate that the proposed method outperforms state-of-the-art approaches in both point cloud denoising and normal filtering.