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Millimeter-wave (mmWave) cell-free massive multiuser (MU) multiple-input multiple-output (MIMO) systems combine the large bandwidths available at mmWave frequencies with the improved coverage of cell-free systems. However, to combat the high path loss at mmWave frequencies, user equipments (UEs) must form beams in meaningful directions, i.e., to a nearby access point (AP). At the same time, multiple UEs should avoid transmitting to the same AP to reduce MU interference. We propose an interference-aware method for beam alignment (BA) in the cell-free mmWave massive MU-MIMO uplink. In the considered scenario, the APs perform full digital receive beamforming while the UEs perform analog transmit beamforming. We evaluate our method using realistic mmWave channels from a commercial ray-tracer, showing the superiority of the proposed method over omnidirectional transmission as well as over methods that do not take MU interference into account.