Compressive X-ray tomosynthesis uses a few two-dimensional projection measurements modulated by coding masks to reconstruct the three-dimensional object that can be sparsely represented on a predefined basis. However, the coding mask optimization and object reconstruction require significant computing resources. In addition, existing methods fall short to exploits the synergy between the encoding and reconstruction stages to approach the global optimum. This paper proposes a model-driven deep learning (MDL) approach to significantly improve the computational efficiency and accuracy of tomosynthesis reconstruction. A unified framework is developed to jointly optimize the coding masks and the neural network parameters, which effectively increase the degrees of optimization freedom. It shows that the computational efficiency of coding mask optimization and image reconstruction can be improved by more than one order of magnitude. Furthermore, the performance of reconstruction results is significantly improved.