Off-road environments remain significant challenges for autonomous ground vehicles, due to the lack of structured roads and the presence of complex obstacles, such as uneven terrain, vegetation, and occlusions. Traditional perception algorithms, primarily designed for structured environments, often fail in unstructured scenarios. In this paper, traversable area recognition is achieved through semantic scene completion. A novel multimodal method, 3DTTNet, is proposed to generate dense traversable terrain estimations by integrating LiDAR point clouds with monocular images from a forward-facing perspective. By integrating multimodal data, environmental feature extraction is strengthened, which is crucial for accurate terrain modeling in complex terrains. Furthermore, RELLIS-OCC, a dataset with 3D traversable annotations, is introduced, incorporating geometric features such as step height, slope, and unevenness. Through a comprehensive analysis of vehicle obsta cle-crossing conditions and the incorporation of vehicle body structure constraints, four traversability cost labels are generated: lethal, medium-cost, low-cost, and free. Experimental results demonstrate that 3DTTNet outperforms the comparison approaches in 3D traversable area recognition, particularly in off-road environments with irregular geometries and partial occlusions. Specifically, 3DTTNet achieves a 42\% improvement in scene completion IoU compared to other models. The proposed framework is scalable and adaptable to various vehicle platforms, allowing for adjustments to occupancy grid parameters and the integration of advanced dynamic models for traversability cost estimation.