The spectrum-efficient millimeter-wave (mmWave) communications has recently attracted much attention as a viable solution to spectrum crunch problem. In this work, we propose a novel non-orthogonal multiple access (NOMA) framework, which makes use of the directional propagation characteristics of mmWave communications so as to improve the spectral efficiency through non-orthogonal signaling. In particular, we consider one-bit quantized angle information as a limited yet effective feedback scheme describing the channel quality of user equipment (UE) in mmWave bands. The UE pairs for NOMA transmission are then established using not only the one-bit distance feedback as a classical approach, but also the one-bit angle feedback. The proposed strategy is therefore referred to as two-bit NOMA. We also propose a novel hybrid strategy, called combined NOMA, for the circumstances with no UE pair through two-bit NOMA. Whenever no UE pair is available through any NOMA strategy, we resort to single user transmission (SUT) with proper UE selection schemes. The hybrid sum-rate performance is also analyzed thoroughly with the respective outage and rate expressions. The numerical results verify that the proposed strategy outperforms one-bit NOMA schemes with either angle- or distance-only feedback.