<p>A three-dimensional description of spin-dependent current transport across nonmagnetic/ferromagnetic interfaces with strong interfacial spin-orbit coupling is presented. The resulting current-induced torques acting on the magnetization of the ferromagnetic layer are addressed. By considering both magnetic exchange and Rashba spin-orbit interactions at the interface, the angular dependence of the spin-orbit torques in Pt/Co and Ta/CoFeB systems is reproduced. In line with two-dimensional Rashba models, the Rashba-Edelstein effect drives the strong field-like torque, with the unconventional angular dependence being most pronounced, when magnetic exchange and spin-orbit interaction strengths are comparable. Furthermore, the spin currents generated through spin-orbit precession and filtering are shown to produce all three spin-polarization components, depending on the magnetization direction. Utilizing these mechanisms in current-in-plane trilayers could potentially enable field-free perpendicular and type-x switching, which is crucial for advancing the miniaturization of spintronic devices.</p>