Three-dimensional (3D) in vitro models have become increasingly popular as systems to study cell-cell and cell-ECM interactions dependent on the spatial, mechanical, and chemical cues within the environment of the tissue, which is limited in traditional two-dimensional (2D) models. Although electrophysiological recordings of neuronal action potentials through 2D microelectrode arrays (MEAs) are a common and trusted method of evaluating neuronal function, network communication, and response to chemicals and biologicals, there are currently limited options for measuring electrophysiological activity from many locations simultaneously throughout a 3D network of neurons in vitro. Here, we have developed a thin-film, 3D flexible microelectrode array (3DMEA) that non-invasively interrogates a 3D culture of neurons and can accommodate 256 channels of recording or stimulation. Importantly, the 3DMEA is straightforward to fabricate and integrates with standard commercially available electrophysiology hardware. Polyimide probe arrays were microfabricated on glass substrates and mechanically actuated to collectively lift the arrays into a vertical position, relying solely on plastic deformation of their base hinge regions to maintain vertical alignment. Human induced pluripotent stem cell (hiPSC)-derived neurons and astrocytes were entrapped in a collagen-based hydrogel and seeded onto the 3DMEA, enabling growth of suspended cells in the matrix and the formation and maturation of a neural network around the 3DMEA probes. The 3DMEA supported the growth of functional neurons in 3D with action potential spike and burst activity recorded over 45 days in vitro. This platform is an important step in facilitating noninvasive electrophysiological characterization of 3D networks of electroactive cells in vitro.