Over the last few years, convolutional neural networks (CNNs) have dominated the field of computer vision thanks to their ability to extract features and their outstanding performance in classification problems, for example in the automatic analysis of X-rays. Unfortunately, these neural networks are considered black-box algorithms, i.e. it is impossible to understand how the algorithm has achieved the final result. To apply these algorithms in different fields and test how the methodology works, we need to use eXplainable AI techniques. Most of the work in the medical field focuses on binary or multiclass classification problems. However, in many real-life situations, such as chest X-rays, radiological signs of different diseases can appear at the same time. This gives rise to what is known as "multilabel classification problems". A disadvantage of these tasks is class imbalance, i.e. different labels do not have the same number of samples. The main contribution of this paper is a Deep Learning methodology for imbalanced, multilabel chest X-ray datasets. It establishes a baseline for the currently underutilised PadChest dataset and a new eXplainable AI technique based on heatmaps. This technique also includes probabilities and inter-model matching. The results of our system are promising, especially considering the number of labels used. Furthermore, the heatmaps match the expected areas, i.e. they mark the areas that an expert would use to make the decision.