Current diagnostic techniques for visualizing bones rely on X-rays, which pose potential harm to both patients and surgical staff. Consequently, the demand for a portable imaging system offering high-resolution, radiation-free, and three-dimensional (3D) imaging capabilities has emerged. This paper introduces a 3D quantitative microwave imaging technique for visualizing musculoskeletal tissue, commonly employed in diagnostic medical imaging. The proposed imaging method is grounded in a set of contrast source (CS) electromagnetic (EM) modeling equations. Through Landweber inverse processing, the solution for the unknown object's electric susceptibility distribution in the modeling equations is derived. The reconstruction process efficiently and effectively generates a 3D image, composed of the object's electric susceptibility distribution. The efficacy of the proposed imaging technique and microwave imaging system is validated through numerical models with both homogeneous and inhomogeneous properties. Moreover, practical validation is performed using a complex multi-layer inhomogeneous phantom within an anechoic chamber. Finally, considering the medical significance of imaging the spine, particularly in cases of car accidents, the proposed Landweber inverse source imaging method and microwave imaging system are practically tested on the human back area, effectively demonstrating their capabilities in imaging musculoskeletal tissue.