Sensing is an integral part of 6G and beyond systems, providing exceptional environmental perception along with communication. Radio frequency (RF)-based sensing often relies on simplified geometric assumptions (e.g., point scatterers or planar surfaces) to model specular multipath and keep inference tractable. However, such representations are limited in their ability to capture extended objects with complex geometries and properties. This paper presents a probabilistic occupancy grid framework for radio-based simultaneous localization and mapping (SLAM), jointly reconstructing geometric structures and their RF-related properties. The proposed occupancy grid map representation is integrated into a multipath-based SLAM formulation to enable simultaneous mobile-agent localization and environment mapping using multipath measurements. To connect RF measurements with the grid map, a surface model is employed to describe candidate reflection paths, while occupancy grid cell states capture measurement uncertainties and fine-grained geometric details. RF-related object properties are represented through reflection coefficients. The proposed framework offers a principled, proof-of-concept approach to physically interpretable radio-based mapping, and simulation results demonstrate accurate reconstruction of geometry and material properties, as well as high-accuracy localization. In addition, the results highlight the potential to use prior occupancy maps obtained from other radio devices or complementary sensors for subsequent map extension and refinement.