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Grasping a variety of objects remains a key challenge in the development of versatile robotic systems. The human hand is remarkably dexterous, capable of grasping and manipulating objects with diverse shapes, mechanical properties, and textures. Inspired by how humans use two fingers to pick up thin and large objects such as fabric or sheets of paper, we aim to develop a gripper optimized for grasping such deformable objects. Observing how the soft and flexible fingertip joints of the hand approach and grasp thin materials, a hybrid gripper design that incorporates both soft and rigid components was proposed. The gripper utilizes a soft pneumatic ring wrapped around a rigid revolute joint to create a flexible two-fingered gripper. Experiments were conducted to characterize and evaluate the gripper performance in handling sheets of paper and other objects. Compared to rigid grippers, the proposed design improves grasping efficiency and reduces the gripping distance by up to eightfold.