This paper investigates the statistical characteristics of the field in the fluctuating transionospheric channel of propagation with intermittency effects taken into account. The intermittency of the ionospheric turbulence is introduced through utilizing the non-Gaussian multifractal stochastic distribution of irregularities of the electron density. As a result of scattering on the intermittent structures, the realizations of the scattered field also reveal intermittent behavior. The propagation problem is simulated utilizing the random screen technique. The statistical characteristics of the field fluctuations after passing the phase screen are studied, and the peculiarities of the field statistics due to the non-Gaussianity of the screen are demonstrated and discussed.