The face inversion effect is typically used to show that faces are processed holistically – when a face is presented upside down it disrupts the perception of identity, expression and eye gaze, even though low-level perceptual features of the image are preserved. We used the inversion effect to investigate how participants perceive the relationship between individual faces. We presented participants with pairs of faces that either looked towards each other (socially engaged) or away from each other (disengaged). We then asked participants to judge where the faces were looking. When the pairs of faces were inverted judgement of engaged pairs was significantly impaired (compared with upright), but the same impairment was not found for inverted disengaged pairs. This selective impairment for engaged pairs suggests that mutual gaze leads to dyads being perceived as perceptual units rather than pairs of discrete individuals.