This paper proposes 3DTTNet, a novel multimodal method for drivable area recognition for autonomous vehicles in unstructured off-road environments. 3DTTNet generates a dense drivable terrain estimation by integrating omnidirectional monocular images and LiDAR point clouds. This involves generating four drivable cost labels: critical, medium, low, and free, taking into account vehicle obstacle clearance conditions and vehicle structural constraints. The RELLIS-OCC dataset, which includes new drivable area annotations, is also presented. Experimental results demonstrate that 3DTTNet outperforms existing methods in 3D drivable area recognition, particularly in off-road environments with irregular geometries and partial occlusion, achieving a 42% improvement in scene completion IoU. The proposed framework is scalable and adaptable to various vehicle platforms, and drivable cost estimation can be improved by tuning occupancy grid parameters and incorporating advanced dynamic models.