In this work an original closed-form approximate evaluation is performed for the continuousspectrum field excited by line and point sources in a dielectric multilayer configuration. By means of a suitable approximate asymptotic representation of the residual-wave field, the continuous-spectrum field has been expressed as the sum of two leaky waves, each weighted by a transition function which depends on both the frequency and the observation distance. This result is uniformly valid in frequency, i.e., both when the leaky wave is physical and in the entire transition region through the spectral gap, and explicitly shows the nature of the continuous spectrum in the transition region, providing insight into the nature of the fields on more complicated structures in microwave integrated circuits.