A theoretical analysis of spontaneous emission from a quantum well in dielectric multilayer structures, especially the influence of dielectric geometry on the relative intensities of guided and radiation modes and on polarization, is presented. We first discuss a relatively simple three-layer case, and subsequently a technologically more interesting five-layer structure that has been proposed for a high-power laser. The expression for the partial, as well as total, emission rates is derived within a broader framework of coupled Heisenberg equations of motion for charge carriers and the quantized electromagnetic field. Thereby, explicit mode decomposition of the Green tensor is avoided. Still, the beta factor for individual guided modes, which is a relevant quantity for the lasing threshold of a device, can be identified and a competition between modes is shown to exist in specific cases.