We report on spin transport in WS2-based 2D-magnetic tunnel junctions (2D-MTJs), unveiling a band structure spin filtering effect specific to the transition metal dichalcogenides (TMDCs) family. WS2 mono-, bi-, and trilayers are derived by a chemical vapor deposition process and further characterized by Raman spectroscopy, atomic force microscopy (AFM), and photoluminescence spectroscopy. The WS2 layers are then integrated in complete Co/Al2O3/WS2/Co MTJ hybrid spin-valve structures. We make use of a tunnel Co/Al2O3 spin analyzer to probe the extracted spin-polarized current from the WS2/Co interface and its evolution as a function of WS2 layer thicknesses. For monolayer WS2, our technological approach enables the extraction of the largest spin signal reported for a TMDC-based spin valve, corresponding to a spin polarization of PCo/WS2 = 12%. Interestingly, for bi- and trilayer WS2, the spin signal is reversed, which indicates a switch in the mechanism of interfacial spin extraction. With the support of ab initio calculations, we propose a model to address the experimentally measured inversion of the spin polarization based on the change in the WS2 band structure while going from monolayer (direct bandgap) to bilayer (indirect bandgap). These experiments illustrate the rich potential of the families of semiconducting 2D materials for the control of spin currents in 2D-MTJs.