This paper presents two new types of transceiver designs for the multi-cell, multi-user, multiple-input-multiple-output (MIMO) interfering broadcast channel (IBC). In contrast to the existing maximum sum rate and max-min fairness transceiver designs, the proposed designs aim at balancing on the two objectives by maximizing the minimum average sum-rate per cell (type-1) or maximizing the minimum average sum-rate within each cell (type-2). Due to the difficulty of these problems, two iterative suboptimal algorithms which ensure local convergence have been proposed. Simulation results show that the proposed algorithms can provide certain level of fairness guarantee without sacrificing much of the overall system performance. As a result, the proposed designs are in some sense more balanced and can be useful alternatives in addition to the existing designs.