We use neutron scattering to show that ferromagnetism and antiferromagnetism coexist in the low T state of the pyrochlore quantum magnet Yb₂Ti₂O₇. While magnetic Bragg peaks evidence long-range static ferromagnetic order, inelastic scattering shows that short-range correlated antiferromagnetism is also present. Small-angle neutron scattering provides direct evidence for mesoscale magnetic structure that we associate with metastable antiferromagnetism. Classical Monte Carlo simulations based on exchange interactions inferred from ⟨111⟩-oriented high-field spin wave measurements confirm that antiferromagnetism is metastable within the otherwise ferromagnetic ground state. The apparent lack of coherent spin wave excitations and strong sensitivity to quenched disorder characterizing Yb₂Ti₂O₇ is a consequence of this multiphase magnetism.