Experiments with layers of salt and sugar solution separated by a diffusive interface are described. Interfacial waves were spontaneously generated by the convection once the system evolved to a critical value of the density-anomaly ratio Rρ≡βΔS/αΔT. The waves locally modulated the interfacial fluxes by modifying the interface thickness and thereby organized otherwise random convective motions into large-scale circulations. In turn, the waves themselves persisted for unusually long times owing to energy input from the organized convection. The dependence of the wave speed on the layer properties and channel dimensions was successfully predicted by assuming that coupling requires a matching of the wave and convection speeds, and that the system selects waves of an amplitude for which this resonance can occur. This ‘wave–convection coupling’ also appeared to increase the interfacial fluxes at low Rρ. The interaction of waves and convection may be important for oceanic thermohaline staircases and other systems where convection is driven by interfacial fluxes.