Network models of cortex typically focus on excitatory population dynamics, relegating inhibition to a support role. However, recent studies have shown that memories can be encoded by both excitatory and inhibitory neurons (EI engrams), adding to the evidence of the functional importance of inhibitory neurons beyond mere stabilization. The functional consequence of such EI engrams is unclear, and the synaptic plasticity rules that could sustain them are unknown. Here, we explore in silico a mechanism for EI engrams storage and recall to glean possible computational benefits of such engrams over the classical, excitatory-only engrams. Towards this end, we consider recurrent spiking networks with Hebbian synaptic plasticity at both inhibitory-to-inhibitory (I-I) and inhibitory-to-excitatory (I-E) synapses. We show that the conjunction of these rules can robustly stabilize embedded EI engrams. Such engrams can then be recalled directly by stimulation of excitatory neurons, or indirectly via disinhibition of inhibitory neurons. Both of these possibilities lead to reliable pattern completion and separation. In the absence of specific cues, networks display asynchronous irregular activity that is robust to perturbations. Finally, we show that–in our hands– similar networks that either lack I-I plasticity or lack an inhibitory part of the engram altogether display much-degraded pattern separation/completion capabilities. Overall, our study broadens the focus to include excitatory and inhibitory neurons in network models of synaptic plasticity, suggesting that inhibitory neurons may play an important role in the recall of memory.