3D reverse engineering is a long sought-after, yet not completely achieved goal in the Computer-Aided Design (CAD) industry. The ultimate objective is to recover the construction history of a CAD model. Starting from a Boundary Representation (B-Rep) of a CAD model, this paper proposes a new deep neural network, CADOps-Net, that jointly learns the CAD operation types and the decomposition into different CAD operation steps. This joint learning allows to divide a B-Rep into parts that were created by various types of CAD operations at the same construction step; therefore providing relevant information for further recovery of the design history. Furthermore, we propose the novel CC3D-Ops dataset that includes over 37k CAD models annotated with CAD operation type labels and step labels. Compared to existing datasets, the complexity and variety of CC3D-Ops models are closer to those used for industrial purposes. Our experiments, conducted on the proposed CC3D-Ops and the publicly available Fusion360 datasets, demonstrate the competitive performance of CADOps-Net with respect to state-of-the-art, and confirm the importance of the joint learning of CAD operation types and steps.