Macroscopic systems forced by the temporal modulation of their parameters exhibit complex interfaces between symmetric states. Here we investigate the origin of the transition from a flat to an oscillating decorated interface. Based on a model that describes a magnetic plane under the influence of an oscillating magnetic field and an extended Josephson junction under the influence of an alternating current, we derive a simple model that accounts for the interface dynamics. Analytically this model allows us to reveal that this transition is a parametric resonance between the frequencies of interface modes and the forcing. Numerical simulations of magnetic systems, extended Josephson junctions, and our simplified model show quite good agreement.