We discuss a joint microscopic theory for the laser-induced magnetization dynamics and spin transport in magnetic heterostructures based on the s-d interaction. Angular momentum transfer is mediated by scattering of itinerant s electrons with the localized (d electron) spins. We use the corresponding rate equations and focus on a spin-12 d electron system, leading to a simplified analytical expression for the dynamics of the local magnetization that is coupled to an equation for the nonequilibrium spin accumulation of the s electrons. We show that this description converges to the microscopic three-temperature model in the limit of a strong s-d coupling. The equation for the spin accumulation is used to introduce diffusive spin transport. The presented numerical solutions show that during the laser-induced demagnetization in a ferromagnetic metal, a short-lived spin accumulation is created that counteracts the demagnetization process. Moreover, the spin accumulation leads to the generation of a spin current at the interface of a ferromagnetic and nonmagnetic metal. Depending on the specific magnetic system, both local spin dissipation and interfacial spin transport are able to enhance the demagnetization rate by providing relaxation channels for the spin accumulation that is built up during demagnetization in the ferromagnetic material.