Laterally resolved measurements of the quantum size effect (QSE) in electron reflectivity are made with low energy electron microscopy on coherently strained Ag films on a W(110) surface. The evolution of the total film thickness with increasing number of atomic layers is determined accurately by dynamical theory analysis of the QSE features. Combined with a model of layer spacings obtained from first-principles calculations, this provides for a novel approach to determine the buried interface layer spacing, which is inaccessible to other methods.