Faces convey a wealth of information essential for social interaction. Their importance has prompted suggestions that some facial features may even be processed unconsciously. Evidence for such unconscious processing has predominantly come from the Breaking Continuous Flash Suppression (b-CFS) paradigm, which measures the time it takes different stimuli to overcome interocular suppression. For instance, suppressed upright faces and faces making eye contact are detected faster than inverted faces and faces looking away, respectively. However, the b-CFS procedure suffers from important problems: Observers can decide how much information they receive before committing to a report, so their detection responses may be influenced by differences in decision criteria and by stimulus identification. Here, we first replicated gaze-direction and face-orientation b-CFS effects, and then developed a new procedure that addresses these problems by using predefined exposure durations and measuring sensitivity and decision criteria for both detection of suppressed stimuli (reporting their location on screen) and identification of those stimuli (reporting gaze direction). Importantly, we find higher detection sensitivity to both upright and direct-gaze (compared to inverted and averted-gaze) faces, with no effects on decisional factors. For identification, however, we find both greater sensitivity and more liberal criteria for upright faces. Our findings demonstrate separable influences of face orientation and gaze direction on detection and identification in the access of faces to awareness, as well as the importance of using methods that can dissociate perceptual and decisional processes.