Inhibitory interneurons, ubiquitous in the central nervous system, form networks connected through both chemical synapses and gap junctions. These networks are essential for regulating the activity of principal neurons, especially by inducing temporally patterned dynamic states. We aim to understand the dynamic mechanisms for synchronisation in networks of electrically and chemically coupled interneurons. We use the exact mean-field reduction to derive a neural mass model for both homogeneous and clustered networks. We first analyse a single population of neurons to understand how the two couplings interact with one another. We demonstrate that the network transitions from an asynchronous to a synchronous regime either by increasing the strength of the gap junction connectivity or the strength of the background input current. Conversely, the strength of inhibitory synapses affects the population firing rate, suggesting that electrical and chemical coupling strengths act as complementary mechanisms by which networks can tune synchronous oscillatory behavior. In line with previous work, we confirm that the depolarizing spikelet is crucial for the emergence of synchrony. Furthermore, find that the fast frequency component of the spikelet ensures robustness to heterogeneity. Next, inspired by the existence of multiple interconnected interneuron subtypes in the cerebellum, we analyse networks consisting of two clusters of cell types defined by differing chemical versus electrical coupling strengths. We show that breaking the electrical and chemical coupling symmetry between these clusters induces bistability, so that a transient external input can switch the network between synchronous and asynchronous firing. Together, our results shows the variety of cell-intrinsic and network properties that contribute to synchronisation of interneuronal networks with multiple types of coupling.