The paper is devoted to the recent developments and extensions of the transionospheric stochastic channel model developed by the authors. The Hybrid Scintillation Propagation Model (HSPM) [1] was created as the combination of the Complex Phase Method (CPM) and rigorous technique of the random (not necessarily phase) screen. The CPM, in turn, is the extension of the classic Rytov's method to the case of the inhomogeneous background medium. In order to correctly describe the special case when the propagation path is oriented close to the direction of the magnetic field lines, i.e., along the strongly elongated ionospheric irregularities, the CPM was extended in [2] to account for the highly anisotropic character of the ionospheric turbulence. Another extension concerns accounting the second order term in the expansion of the complex phase method employed in CPM. The effect is that, in distinction from the commonly accepted Gaussian distribution of the complex phase in the first order approximation, the accounting of the second order term produces the deviation of the distribution from the Gaussianity. The main effects are the shift of the mean and skewness of the probability density function of the log-amplitude distribution after passing the turbulent layer. These effects can be quantitatively characterized utilizing the higher cumulants of the distribution that are derived employing the second order terms of the complex phase expansion [3]. In particular, the third cumulant characterizes the skewness of the distribution. This distribution is then utilized in the algorithm [4] of generating the corresponding non-Gaussian distribution of the random field realizations on the screen, introduced below the ionosphere according to the HSPM technique. The extensions mentioned lead to the random field distributions different of those obtained, if the effects of the anisotropy and deviation from Gaussianity were not properly taken into account. In turn, this finally results in the different field distribution and values of the scintillation indices for the random field observed on the Earth's surface. In the paper, the details of the analytical derivations and results of simulation making use of the extended HSPM model will be presented and discussed.