The segmentation of brain tissues based on MRI data represents a widely investigated problem in medical image analysis. Infant brain tissues in the so-called isointense phase of development, around the age of 6 to 9 months, are difficult to segment due to the inherent myelination and maturation processes, which manifest in grey and white matter pixel intensity distributions severely overlapping in both T1-weighted and T2-weighted MRI data. This paper introduces two different U-net architectures, one with 2D convolution and this other with 3D convolution, and employs them in infant brain tissue segmentation based on multi-spectral MRI data. The proposed methods are trained and tested on the training data set of the iSeg-2017 challenge. All records were initially fed to histogram alignment that was independently performed on each data channel. Nine records were used for training and one record for testing in each evaluation round, but all ten records took their turn as testing data. Statistical accuracy indicators were employed to assess the segmentation accuracy of both network models. The U-net architecture preforming 3D convolution obtained the better segmentation, achieving 91.8% average rate of correct decisions, and 95.0%, 91.5% and 89.8% Dice similarity score for cerebrospinal fluid, grey matter, and white matter tissues, respectively.