In our work, we numerically investigated how the roughness of interfaces between different layers in 3D layered models affects the upscaled and downscaled elastic properties. We considered layered models with random rough interfaces and fixed elastic properties in the background and the middle layer, upscaled them to compute the effective stiffness tensor and then downscaled them to obtain new elastic parameters of the middle layer in the statistically equivalent models with smooth interfaces. Afterward, we investigated the dependence of the obtained results on four input varied parameters (the correlation length, standard deviation of the roughness and two physical elastic parameters of the middle layer). Next, we proposed an algorithm for recovering the covariance matrix of such stiffness tensors for arbitrary values from the four-parameter space, applying bilinear regression to the parameters of the interface and the linear component-by-component interpolation by two nearest points to the material parameters. Verification of this algorithm showed that for limited standard deviation values the errors in restoring the covariance matrix do not exceed 0.07. Thus, smooth interface models with random material parameters in the middle layer can be statistically simulated with arbitrary values of the input parameters with high accuracy.