The nonlinear propagation of coupled Langmuir and dust-acoustic waves in a multi-component dusty plasma is considered. The coupled mode propagation is described by a Schrödinger–Boussinesq system, which reduces to the Schrödinger–KdV system for unidirectional wave propagation. For stationary propagation, the coupled waves are governed by a generic Hamiltonian that is integrable in both sub- and the supersonic regimes of Mach number. Depending on the parameter regimes, exact analytical solutions for the coupled waves having single-, double- and triple-hump structures for the Langmuir field intensity are obtained. The exact governing equations for large-amplitude waves are also derived, and are solved approximately. The existence conditions for large-amplitude localized solutions in the quasineutral limit are discussed.