Two-way is a dominant mode of communication in wireless systems. Departing from the tradition to optimize each transmission direction separately, recent work has demonstrated that, for time-division duplex (TDD) systems, optimizing the schedule of the two transmission directions depending on traffic load and interference condition leads to performance gains. In this letter, a general network of multiple interfering two-way links is studied under the assumption of a balanced load in the two directions for each link. Using the notion of interference spin, we introduce an algebraic framework for the optimization of two-way scheduling, along with an efficient optimization algorithm that is based on the pruning of a properly defined topology graph and dynamic programming. Numerical results demonstrate multi-fold rate gains with respect to baseline solutions, especially for worst-case (5%-ile) rates.