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Multiple object detection and pose estimation are vital computer vision tasks. The latter relates to the former as a downstream problem in applications such as robotics and autonomous driving. However, due to the high complexity of both tasks, existing methods generally treat them independently, which is sub-optimal. We propose simultaneous neural modeling of both using monocular vision and 3D model infusion. Our Simultaneous Multiple Object detection and Pose Estimation network (SMOPE-Net) is an end-to-end trainable multitasking network with a composite loss that also provides the advantages of anchor-free detections for efficient downstream pose estimation. To enable the annotation of training data for our learning objective, we develop a Twin-Space object labeling method and demonstrate its correctness analytically and empirically. Using the labeling method, we provide the KITTI-6DoF dataset with $\sim7.5$K annotated frames. Extensive experiments on KITTI-6DoF and the popular LineMod datasets show a consistent performance gain with SMOPE-Net over existing pose estimation methods. Here are links to our proposed SMOPE-Net, KITTI-6DoF dataset, and LabelImg3D labeling tool.