Three-dimensional in vitro models in microfluidic systems are promising tools for studying cell biology, with complex models using multiple cell types combined with high resolution imaging. Neuronal models demand electrical readout of the activity of networks of single neurons, yet classical planar microelectrode arrays struggle to capture extracellular action potentials when neural soma are suspended distant from the microelectrodes. This study introduces sophisticated microfluidic microelectrode arrays, specifically tailored for electrophysiology of 3D neuronal cultures. Using multilayer photolithography of permanent epoxy photoresists, we developed devices having 12 independent culture modules in a convenient format. Each module has two adjacent compartments for hydrogel-based 3D cell culture, with tunnels allowing projection of neurites between compartments. Microelectrodes integrated in the tunnels record action potentials as they pass between the compartments. Mesh ceilings separate the compartments from overlying wells, allowing for simple cell seeding and later nutrient, gas and waste exchange and application of test substances. Using these devices, we have demonstrated 3D neuronal culture, including electrophysiological recording and live imaging. This microphysiological platform will enable high-throughput investigation of neuronal networks for investigation of neurological disorders, neural pharmacology and basic neuroscience. Further models could include cocultures representing multiple brain regions or innervation models of other organs.