Room temperature ferromagnetism has been obtained for different sets of Mn/Si3N4 multilayers prepared by sputtering. In order to find the most suitable conditions to stabilize the ferromagnetic ordering in this system, the evolution of the magnetic properties has been studied for films in which the Si3N4 layer thickness was maintained constant while that of the Mn layer was varied, [Mn(tm)/Si3N4(3.4 nm)]n, and conversely, in [Mn(0.7 nm)/Si3N4(tsn)]43 samples, in which the Mn layer thickness was kept constant while varying the Si3N4 layer thickness. Structural, compositional, electronic and magnetic characterizations have been performed by means of x-ray reflectometry, Rutherford backscattering spectrometry, x-ray photoemission spectroscopy, x-ray absorption, and superconducting quantum interference device for further knowledge of the magnetic-structural relationship in this system. Our results show that the peculiar magnetic behavior of these films is mainly related to the stabilization of a slightly distorted Mn3N2 phase that is induced by the Si3N4 at the interfaces. For samples with larger Mn layer thickness, metallic Mn and Mn3N2 phases coexist, which leads to a reduction of the total magnetization per Mn atom due to the presence of metallic Mn. For small Mn layer thickness (tm<0.86 nm), where noncontinuous Mn3N2 layers are formed, the magnetization decreases noticeably due to the superparamagnetic size limit. It has been found that the best conditions for the stabilization of the ferromagnetism in this system occur when both, the manganese-rich and the silicon nitride layers, are continuous and with similar thickness, close to 3.5 nm.