Collaborative learning methods for medical image segmentation are often variants of UNet, where the constructions of classifiers depend on each other and their outputs are supervised independently. However, they cannot explicitly ensure that optimizing auxiliary classifier heads leads to improved segmentation of target classifier. To resolve this problem, we propose a structured collaborative learning (SCL) method, which consists of a context-aware structured classifier population generation (CA-SCPG) module, where the feature propagation of the target classifier path is directly enhanced by the outputs of auxiliary classifiers via a light-weighted high-level context-aware dense connection (HLCA-DC) mechanism, and a knowledge-aware structured classifier population supervision (KA-SCPS) module, where the auxiliary classifiers are properly supervised under the guidance of target classifier's segmentations. Specifically, SCL is proposed based on a recurrent-dense-siamese decoder (RDS-Decoder), which consists of multiple siamese-decoder paths. CA-SCPG enhances the feature propagation of the decoder paths by HLCA-DC, which densely reuses previous decoder paths' output prediction maps to belong to the target classes as inputs to the layers of latter decoder paths. KA-SCPS supervises the classifier heads simultaneously with KA-SCPS loss, which consists of a generalized weighted cross-entropy loss for deep class-imbalanced learning and a novel knowledge-aware Dice loss (KA-DL). KA-DL is a weighted Dice loss broadcasting knowledges learnt by the target classifier to other classifier heads, harmonizing the learning process of the classifier population. Experiments are performed based on PET/CT volumes with malignant melanoma, lymphoma, or lung cancer. Experimental results demonstrate the superiority of our SCL, when compared to the state-of-the-art methods and baselines.