Traditional three-dimensional (3D) bioprinting has always been associated with the challenge of print fidelity of complex geometries due to the gel-like nature of the bioinks. Embedded 3D bioprinting has emerged as a potential solution to print complex geometries using proteins and polysaccharides-based bioinks. This study demonstrated the Freeform Reversible Embedding of Suspended Hydrogels (FRESH) 3D bioprinting method of chitosan bioink to 3D bioprint complex geometries. 4.5% chitosan was dissolved in an alkali solvent to prepare the bioink. Rheological evaluation of the bioink described its shear-thinning nature. The power law equation was fitted to the shear rate-viscosity plot. The flow index value was found to be less than 1, categorizing the material as pseudo-plastic. The chitosan bioink was extruded into another medium, a thermo-responsive 4.5% gelatin hydrogel. This hydrogel supports the growing print structures while printing. After this, the 3D bioprinted structure was crosslinked with hot water to stabilize the structure. Using this method, we have 3D bioprinted complex biological structures like the human tri-leaflet heart valve, a section of a human right coronary arterial tree, a scale-down outer structure of the human kidney, and a human ear. Additionally, we have shown the mechanical tunability and suturability of the 3D bioprinted structures. This study demonstrates the capability of the chitosan bioink and FRESH method for 3D bioprinting of complex biological models for biomedical applications.