Materials with broad absorption bands are highly desirable for electromagnetic filtering and processing applications, especially if the absorption can be externally controlled. Here, a new class of broadband-absorption materials is introduced. Namely, layered metamagnets exhibit an electromagnetic excitation continuum in the magnetic-field-induced mixed ferro- and antiferromagnetic phase. Employing a series of complementary experimental techniques involving neutron scattering, muon spin relaxation, specific heat, ac and dc magnetization measurements, and electron magnetic resonance, a detailed magnetic phase diagram of Cu₃Bi(SeO₃)₂O₂Br is determined and it is found that the excitations in the mixed phase extend over at least ten decades of frequency. The results, which reveal a new dynamical aspect of the mixed phase in metamagnets, open up a novel approach to controllable microwave filtering.