Praying mantids are the only insects proven to have stereoscopic vision (stereopsis): the ability to perceive depth from the slightly shifted images seen by the two eyes. Recently, the first neurons likely to be involved in mantis stereopsis were described and a speculative neuronal circuit suggested. Here we further investigate classes of neurons in the lobula complex of the praying mantis brain and their tuning to stereoscopically-defined depth. We used sharp electrode recordings with tracer injections to identify visual projection neurons with input in the optic lobe and output in the central brain. In order to measure binocular response fields of the cells the animals watched a vertical bar stimulus in a 3D insect cinema during recordings. We describe the binocular tuning of 19 neurons projecting from the lobula complex and the medulla to central brain areas. The majority of neurons (12/19) were binocular and had receptive fields for both eyes that overlapped in the frontal region. Thus, these neurons could be involved in mantis stereopsis. We also find that neurons preferring different contrast polarity (bright vs dark) tend to be segregated in the mantis lobula complex, reminiscent of the segregation for small targets and widefield motion in mantids and other insects.