We present an electrophysiological model of double bouquet cells and integrate them into an established cortical columnar microcircuit model that has previously been used as a spiking attractor model for memory. Learning in that model relies on a Hebbian-Bayesian learning rule to condition recurrent connectivity between pyramidal cells. We here demonstrate that the inclusion of a biophysically plausible double bouquet cell model can solve earlier concerns about learning rules that simultaneously learn excitation and inhibition and might thus violate Dale's principle. We show that learning ability and resulting effective connectivity between functional columns of previous network models is preserved when pyramidal synapses onto double bouquet cells are plastic under the same Hebbian-Bayesian learning rule. The proposed architecture draws on experimental evidence on double bouquet cells and effectively solves the problem of duplexed learning of inhibition and excitation by replacing recurrent inhibition between pyramidal cells in functional columns of different stimulus selectivity with a plastic disynaptic pathway. We thus show that the resulting change to the microcircuit architecture improves the model's biological plausibility without otherwise impacting the model's spiking activity, basic operation, and learning abilities.