Three-node full-duplex is a promising new transmission mode between a full-duplex capable wireless node and two other wireless nodes that use half-duplex transmission and reception respectively. Although three-node full-duplex transmissions can increase the spectral efficiency without requiring full-duplex capability of user devices, inter-node interference - in addition to the inherent self-interference - can severely degrade the performance. Therefore, as methods that provide effective self-interference mitigation evolve, the management of inter-node interference is becoming increasingly important. This paper considers a cellular system in which a full-duplex capable base station serves a set of half-duplex capable users. As the spectral efficiencies achieved by the uplink and downlink transmissions are inherently intertwined, the objective is to device channel assignment and power control algorithms that maximize the weighted sum of the uplink-downlink transmissions. To this end a distributed auction based channel assignment algorithm is proposed, in which the scheduled uplink users and the base station jointly determine the set of downlink users for full-duplex transmission. Realistic system simulations indicate that the spectral efficiency can be up to 89% better than using the traditional half-duplex mode. Furthermore, when the self-interference cancelling level is high, the impact of the user-to-user interference is severe unless properly managed.