The magnetization reversal and spin structure in circular Co/insulator/Ni80Fe20 trilayer dots has been investigated numerically. The effect of dipolar coupling between a soft ferromagnetic Permalloy (Py=Ni80Fe20) layer and a hard ferromagnetic Cobalt layer inside one stack is studied. We find either a stabilization or even a triggering of the vortex state in the Py layer due to the magnetic stray field of the Co layer, while the Co magnetization remains in a single-domain state. Furthermore, for thin Py layers a 360 deg-domain wall is observed. We construct a phase diagram, where regions of vortex stabilization, triggering, and occurrence of a 360 deg domain wall are marked.