On the basis of first-principles electronic-structure calculations we predict that epitaxial multiferroic films - fabricated as ultrathin Fe films deposited on TiO₂-terminated (001) surfaces of ATiO₃ perovskites (A = Pb, Ba) - exhibit an unexpected change in their magnetic structure with increasing Fe-film thickness. The magnetic order changes from ferromagnetic, with a magnetization of about 3 μ_B/atom for the 1 ML system, to ferrimagnetic with almost vanishing magnetization upon deposition of a second Fe layer. Ferromagnetic order is restored for thicker Fe films but with significantly reduced magnetization as compared to Fe bulk. The effect is understood in terms of hybridization of electronic states and geometric structure. The magnetoelectric coupling affects the size of the magnetic moments moderately; a spin-reorientation transition is not found.