Numerous dual-energy CT (DECT) techniques have been developed in the past few decades. Dual-energy CT (DECT) statistical iterative reconstruction (SIR) has demonstrated its potential for reducing noise and increasing accuracy. Our lab proposed a joint statistical DECT algorithm for stopping power estimation and showed that it outperforms competing image-based material-decomposition methods. However, due to its slow convergence and the high computational cost of projections, the elapsed time of 3D DECT SIR is often not clinically acceptable. Therefore, to improve its convergence, we have embedded DECT SIR into a deep learning model-based unrolled network for 3D DECT reconstruction (MB-DECTNet) that can be trained in an end-to-end fashion. This deep learning-based method is trained to learn the shortcuts between the initial conditions and the stationary points of iterative algorithms while preserving the unbiased estimation property of model-based algorithms. MB-DECTNet is formed by stacking multiple update blocks, each of which consists of a data consistency layer (DC) and a spatial mixer layer, where the spatial mixer layer is the shrunken U-Net, and the DC layer is a one-step update of an arbitrary traditional iterative method. Although the proposed network can be combined with numerous iterative DECT algorithms, we demonstrate its performance with the dual-energy alternating minimization (DEAM). The qualitative result shows that MB-DECTNet with DEAM significantly reduces noise while increasing the resolution of the test image. The quantitative result shows that MB-DECTNet has the potential to estimate attenuation coefficients accurately as traditional statistical algorithms but with a much lower computational cost.