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Change detection is one of the most active research areas in Remote Sensing (RS). Most of the recently developed change detection methods are based on deep learning (DL) algorithms. This kind of algorithms is generally focused on generating two-dimensional (2D) change maps, thus only identifying planimetric changes in land use/land cover (LULC) and not considering nor returning any information on the corresponding elevation changes. Our work goes one step further, proposing two novel networks, able to solve simultaneously the 2D and 3D CD tasks, and the 3DCD dataset, a novel and freely available dataset precisely designed for this multitask. Particularly, the aim of this work is to lay the foundations for the development of DL algorithms able to automatically infer an elevation (3D) CD map -- together with a standard 2D CD map --, starting only from a pair of bitemporal optical images. The proposed architectures, to perform the task described before, consist of a transformer-based network, the MultiTask Bitemporal Images Transformer (MTBIT), and a deep convolutional network, the Siamese ResUNet (SUNet). Particularly, MTBIT is a transformer-based architecture, based on a semantic tokenizer. SUNet instead combines, in a siamese encoder, skip connections and residual layers to learn rich features, capable to solve efficiently the proposed task. These models are, thus, able to obtain 3D CD maps from two optical images taken at different time instants, without the need to rely directly on elevation data during the inference step. Encouraging results, obtained on the novel 3DCD dataset, are shown. The code and the 3DCD dataset are available at https://sites.google.com/uniroma1.it/3dchangedetection/home-page.