Ga1-xMnxAs/AlAs multiple quantum wells (MQWs) with Mn concentrations of x=0.03 and x=0.043 are grown by low-temperature molecular beam epitaxy on GaAs(100) surfaces. We establish the optimum growth conditions by carefully determining the corresponding As partial pressure and growth temperature. The samples are characterized by x-ray diffraction in conjunction with simulations based on the dynamical diffraction theory to determine the structural and compositional parameters of the MQWs. High resolution transmission electron microscopy is used to analyze the microstructure of the MQWs and, in particular, to measure the interface roughness. Magnetic measurements reveal that the grown samples show ferromagnetic behavior.