Achieving human-like dexterity in robotic grippers remains an open challenge, particularly in ensuring robust manipulation in uncertain environments. Soft robotic hands try to address this by leveraging passive compliance, a characteristic that is crucial to the adaptability of the human hand, to achieve more robust manipulation while reducing reliance on high-resolution sensing and complex control. Further improvements in terms of precision and postural stability in manipulation tasks are achieved through the integration of variable stiffness mechanisms, but these tend to lack residual compliance, be bulky and have slow response times. To address these limitations, this work introduces a Compliant Joint Jamming mechanism for anthropomorphic fingers that exhibits passive residual compliance and adjustable stiffness, while achieving a range of motion in line with that of human interphalangeal joints. The stiffness range provided by the mechanism is controllable from 0.48 Nm/rad to 1.95 Nm/rad (a 4x increase). Repeatability, hysteresis and stiffness were also characterized as a function of the jamming force. To demonstrate the importance of the passive residual compliance afforded by the proposed system, a peg-in-hole task was conducted, which showed a 60% higher success rate for a gripper integrating our joint design when compared to a rigid one.