This paper considers the problem of Hierarchical Multilabel Classification (HMC), where (i) several labels can be present for each example, and (ii) labels are related via a domain-specific hierarchy tree. Guided by the intuition that all mistakes are not equal, we present Comprehensive Hierarchy Aware Multilabel Predictions (CHAMP), a framework that penalizes a misprediction depending on its severity as per the hierarchy tree. While such an approach has been applied to single-label classification, to the best of our knowledge, there is no work extending it to the general multilabel setting. A key challenge here is to identify a metric that quantifies the discrepancy between the sets of predicted labels and ground truth labels as per the given hierarchy tree. We address this challenge by proposing an assignment strategy for each predicted label to the set of ground truth labels, which naturally leads to CHAMP. Extensive experiments on six public HMC datasets across modalities (image, audio, and text) show that CHAMP significantly reduces the severity of mistakes, as measured by hierarchical metrics, by \(18\%\) on average across datasets. This improvement is achieved without a drop in classification performance over the standard (hierarchy-free) multilabel classification. We provide insights into the gains in hierarchical metrics by attributing them to hierarchy and co-occurrence information in the data.