A magnetic-field-line-integrated model of plasma interchange instabilities is developed for the high latitude ionosphere including magnetospheric coupling effects. We show that the primary magnetosphere-ionosphere coupling effect is to incorporate the inertia of the magnetospheric plasma in the analysis. As a specific example, we present the first simulation of the instability in the inertial regime, i.e., νi « ω where νi is the ion-neutral collision frequency and ω is the wave frequency. We find that the inertial instability develops in a fundamentally different manner than in the collisional case (νi » ω). Our results show that striations produced in the inertial regime are spread and retarded by ion inertial effects, and result in more isotropic irregularities than those seen in the collisional case.