Finger pose offers promising opportunities to expand human computer interaction capability of touchscreen devices. Existing finger pose estimation algorithms that can be implemented in portable devices predominantly rely on capacitive images, which are currently limited to estimating pitch and yaw angles and exhibit reduced accuracy when processing large-angle inputs (especially when it is greater than 45 degrees). In this paper, we propose BiFingerPose, a novel bimodal based finger pose estimation algorithm capable of simultaneously and accurately predicting comprehensive finger pose information. A bimodal input is explored, including a capacitive image and a fingerprint patch obtained from the touchscreen with an under-screen fingerprint sensor. Our approach leads to reliable estimation of roll angle, which is not achievable using only a single modality. In addition, the prediction performance of other pose parameters has also been greatly improved. The evaluation of a 12-person user study on continuous and discrete interaction tasks further validated the advantages of our approach. Specifically, BiFingerPose outperforms previous SOTA methods with over 21% improvement in prediction performance, 2.5 times higher task completion efficiency, and 23% better user operation accuracy, demonstrating its practical superiority. Finally, we delineate the application space of finger pose with respect to enhancing authentication security and improving interactive experiences, and develop corresponding prototypes to showcase the interaction potential. Our code will be available at https://github.com/XiongjunGuan/DualFingerPose.