Depth perception of transparent and reflective objects has long been a critical challenge in robotic manipulation.Conventional depth sensors often fail to provide reliable measurements on such surfaces, limiting the performance of robots in perception and grasping tasks. To address this issue, we propose a novel depth completion network,HDCNet,which integrates the complementary strengths of Transformer,CNN and Mamba architectures.Specifically,the encoder is designed as a dual-branch Transformer-CNN framework to extract modality-specific features. At the shallow layers of the encoder, we introduce a lightweight multimodal fusion module to effectively integrate low-level features. At the network bottleneck,a Transformer-Mamba hybrid fusion module is developed to achieve deep integration of high-level semantic and global contextual information, significantly enhancing depth completion accuracy and robustness. Extensive evaluations on multiple public datasets demonstrate that HDCNet achieves state-of-the-art(SOTA) performance in depth completion tasks.Furthermore,robotic grasping experiments show that HDCNet substantially improves grasp success rates for transparent and reflective objects,achieving up to a 60% increase.