Discontinuous precipitation (DP) was found to initiate at both η′-η′ interphase and η′-η′ grain boundaries in a two-phase Zn-6.3at.% Ag alloy consisting of ε and supersaturated η′ phases. The η′-ε interphase boundaries at which DP has initiated illustrated a sinusoidal interface during ageing, which implies that the morphological instability is a prerequisite for the DP initiation at an η′-ε interphase boundary. The application of the morphological instability model for solid-solid interfaces has indicated that the interface protuberances grow into the supersaturated η′ and the interphase boundary becomes unstable since the observed wavelength of serrated η′-ε interphase boundaries was larger than the critical value predicted by the model. A solute-depleted region is therefore established in front of the η′-ε interphase boundary, which provides an appropriate site leading to a DP reaction. Based on this, a nucleation mechanism of DP at the interphase boundaries is proposed accordingly: the allotriomorphs of DP can be directly developed from ε protuberances of a serrated interphase boundary.