There have been recent works on enabling in-band full-duplex operation using millimeter-wave (mmWave) transceivers. These works are based solely on creating sufficient isolation between a transceiver's transmitter and receiver via multiple-input multiple-output (MIMO) precoding and combining. In this work, we propose supplementing these beamforming strategies with analog self-interference cancellation (A-SIC). By leveraging A-SIC, a portion of the self-interference is cancelled without the need for beamforming, allowing for more optimal beamforming strategies to be used in serving users. We use simulation to demonstrate that even with finite resolution A-SIC solutions, there are significant gains to be had in sum spectral efficiency. With a single bit of A-SIC resolution, improvements over a beamforming-only design are present. With 8 bits of A-SIC resolution, our design nearly approaches that of ideal full-duplex operation. To the best of our knowledge, this is the first mmWave full-duplex design that combines both beamforming and A-SIC to achieve simultaneous transmission and reception in-band.