Tsunoda and Cosgrove <2001> recently pointed out that the F layer and sporadic E (Es) layers in the nighttime midlatitude ionosphere must be considered electrodynamically as a coupled system in light of the presence of a Hall polarization process in Es layers <Haldoupis et al., 1996; Tsunoda, 1998; Cosgrove and Tsunoda, 2001, 2002a> and the fact that kilometer-scale electric fields map efficiently between the E and F regions. They further noted the apparent presence of positive feedback between processes in those regions. Cosgrove and Tsunoda <2002b, 2003> have since shown that Es layers are unstable with properties not unlike those of the Perkins instability in the F region <Perkins, 1973>, thus providing yet another reason to consider the behavior of the coupled system. In this paper we show mathematically that the coupled system is indeed unstable with properties that are not only related to but distinct from those of the individual instabilities. A key finding is that this coupled response significantly enhances the growth rate of F region structures, beyond that of the Perkins instability.