The angular momentum currents have three distinct forms known as the electron spin current, the incoherent magnon current and the coherent macroscopic magnon current. We present a unified theory to correlate these different angular momentum currents in magnetic multilayered structures by using semi-classical approaches for electrons and magnons. Within each layer, which could be magnetic or non-magnetic and metallic or insulating, the non-equilibrium electron or magnon distributions satisfy the Boltzmann equations for fermions and bosons. The momentum and angular momentum transfer among electrons, incoherent magnons, and order parameters are explicitly taken into account via collision terms. By establishing boundary conditions for spin chemical potentials and the angular momentum current at the interfaces, we determine the distributions and subsequently find the spatial dependence of angular momentum currents. The formalism is applied to various multilayer systems and a few predictions are outlined.