Route balancing addresses fair workloads allocation among stakeholders to balance utilization of transportation resources and to guarantee equity among employees. Drop-and-pull transportation has been verified to be beneficial in container drayage and has gradually received attentions from the scientific literature. A container drayage problem that simultaneously considers the drop-and-pull mode and the issue of route balancing is investigated. In the problem, apart from the economic objectives, balanced distribution of workloads from social perspective is especially pursued. A mixed-integer programming model is formulated and a matheuristic algorithm is developed based on embedding the model in a heuristic framework to solve the problem. A division approach is designed to transform the original problem into sub-problems to ease the solving pressure. A fix-and-optimize method is adopted to further reduce the computational burdens from substantial decision variables. The proposed algorithm is tested on solving different application scenarios as single- and multi-trailer drop-and-pull problems. Experimental results indicate that the algorithm can provide much better solutions in shorter computational time when compared to standard approaches.