In this paper, we consider the problem of finding minimal realizations of multivariable linear stable discrete-time systems which interpolate the given first- and second-order information. We present the condition for the existence of a solution to this interpolation problem, the discriminant of its uniqueness and a parametrization of the class of all the solutions. The results may be applied to the design of digital filters, model reduction preserving stability, and the ARMA modelling of multivariable systems.