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We analyze the regression accuracy of convolutional neural networks assembled from encoders, decoders and skip connections and trained with multifidelity data. These networks benefit from a significant reduction in the number of trainable parameters with respect to an equivalent fully connected network. These architectures are also versatile with respect to the input and output dimensionality. For example, encoder-decoder, decoder-encoder or decoder-encoder-decoder architectures are well suited to learn mappings between input and outputs of any dimensionality. We demonstrate the accuracy produced by such architectures when trained on a few high-fidelity and many low-fidelity data generated from models ranging from one-dimensional functions to Poisson equation solvers in two-dimensions. We finally discuss a number of implementation choices that improve the reliability of the uncertainty estimates generated by a dropblock regularizer, and compare uncertainty estimates among low-, high- and multi-fidelity approaches.