Soft robotic hands with integrated sensing capabilities hold great potential for interactive operations. Previous work has typically focused on integrating sensors with fingers. The palm, as a large and crucial contact region providing mechanical support and sensory feedback, remains underexplored due to the currently limited sensing density and interaction with the fingers. Here, we develop a sensorized robotic hand that integrates a high-density tactile palm, dexterous soft fingers, and cooperative palm-finger interaction strategies. The palm features a compact visual-tactile design to capture delicate contact information. The soft fingers are designed as fiber-reinforced pneumatic actuators, each providing two-segment motions for multimodal grasping. These features enable extensive palm-finger interactions, offering mutual benefits such as improved grasping stability, automatic exquisite surface reconstruction, and accurate object classification. We also develop palm-finger feedback strategies to enable dynamic tasks, including planar object pickup, continuous flaw detection, and grasping pose adjustment. Furthermore, our development, augmented by artificial intelligence, shows improved potential for human-robot collaboration. Our results suggest the promise of fusing rich palm tactile sensing with soft dexterous fingers for advanced interactive robotic operations. Robotic hands with tactile sensing hold potential for interactive operations, yet palm sensing remains underexplored. Here, authors present a robotic hand that integrates a high-density tactile palm with soft, dexterous fingers, enhancing palm-finger coordination for improved robotic operation and perception.