The effects of anomalous dispersion (resonance) on multiple reflection of x rays and their interference in crystals at atomic absorption edges are studied. Intensity ratios of two inversion-symmetry-related multiple diffractions at or near absorption edges exhibit highly phase-sensitive profiles with strong asymmetric characteristics, unlike those far from the edges. A new resonance perturbation Bethe approach is developed to explain this behavior. This leads to direct determination of the phase change for x-ray reflections at resonance.