High-fidelity personalized human musculoskeletal models are crucial for simulating realistic behavior of physically coupled human-robot interactive systems and verifying their safety-critical applications in simulations before actual deployment, such as human-robot co-transportation and rehabilitation through robotic exoskeletons. Identifying subject-specific Hill-type muscle model parameters and bone dynamic parameters is essential for a personalized musculoskeletal model, but very challenging due to the difficulty of measuring the internal biomechanical variables in vivo directly, especially the joint torques. In this paper, we propose using Differentiable MusculoSkeletal Model (Diff-MSM) to simultaneously identify its muscle and bone parameters with an end-to-end automatic differentiation technique differentiating from the measurable muscle activation, through the joint torque, to the resulting observable motion without the need to measure the internal joint torques. Through extensive comparative simulations, the results manifested that our proposed method significantly outperformed the state-of-the-art baseline methods, especially in terms of accurate estimation of the muscle parameters (i.e., initial guess sampled from a normal distribution with the mean being the ground truth and the standard deviation being 10% of the ground truth could end up with an average of the percentage errors of the estimated values as low as 0.05%). In addition to human musculoskeletal modeling and simulation, the new parameter identification technique with the Diff-MSM has great potential to enable new applications in muscle health monitoring, rehabilitation, and sports science.