The non-commutative nature of 3D rotations poses well-known challenges in generalizing planar problems to three-dimensional ones, even more so in contact-rich tasks where haptic information (i.e., forces/torques) is involved. In this sense, not all learning-based algorithms that are currently available generalize to 3D orientation estimation. Non-linear filters defined on $\mathbf{\mathbb{SO}(3)}$ are widely used with inertial measurement sensors; however, none of them have been used with haptic measurements. This paper presents a unique complementary filtering framework that interprets the geometric shape of objects in the form of superquadrics, exploits the symmetry of $\mathbf{\mathbb{SO}(3)}$, and uses force and vision sensors as measurements to provide an estimate of orientation. The framework's robustness and almost global stability are substantiated by a set of experiments on a dual-arm robotic setup.