We study inserting Co layer thickness-dependent spin transport and spin-orbit torques (SOTs) in the Pt/Co/Py trilayers by spin-torque ferromagnetic resonance. The interfacial perpendicular magnetic anisotropy (IPMA) energy density (K
s = 2.7 erg/cm2), which is dominated by interfacial spin-orbit coupling (ISOC) in the Pt/Co interface, total effective spin-mixing conductance (G
eff,tot
↑↓=0.42×15 Ω-1 m-2) and two-magnon scattering (β
TMS= 0.46 nm2) are first characterized, and the damping-like torque (ξDL= 0.103) and field-like torque (ξFL=-0.017) efficiencies are also calculated quantitatively by varying the thickness of the inserting Co layer. The significant enhancement of ξDL and ξFL in Pt/Co/Py than Pt/Py bilayer system originates from the interfacial Rashba-Edelstein effect due to the strong ISOC between Co-3d and Pt-5d orbitals at the Pt/Co interface. Additionally, we find a considerable out-of-plane spin polarization SOT, which is ascribed to the spin anomalous Hall effect and possible spin precession effect due to IPMA-induced perpendicular magnetization at the Pt/Co interface. Our results demonstrate that the ISOC of the Pt/Co interface plays a vital role in spin transport and SOTs-generation. Our finds offer an alternative approach to improve the conventional SOTs efficiencies and generate unconventional SOTs with out-of-plane spin polarization to develop low power Pt-based spintronic via tailoring the Pt/FM interface.