In this paper, we strive to answer the question "how to collaboratively learn convolutional neural network (CNN)-based and vision transformer (ViT)-based models by selecting and exchanging the reliable knowledge between them for semantic segmentation?" Accordingly, we propose an online knowledge distillation (KD) framework that can simultaneously learn compact yet effective CNN-based and ViT-based models with two key technical breakthroughs to take full advantage of CNNs and ViT while compensating their limitations. Firstly, we propose heterogeneous feature distillation (HFD) to improve students' consistency in low-layer feature space by mimicking heterogeneous features between CNNs and ViT. Secondly, to facilitate the two students to learn reliable knowledge from each other, we propose bidirectional selective distillation (BSD) that can dynamically transfer selective knowledge. This is achieved by 1) region-wise BSD determining the directions of knowledge transferred between the corresponding regions in the feature space and 2) pixel-wise BSD discerning which of the prediction knowledge to be transferred in the logit space. Extensive experiments on three benchmark datasets demonstrate that our proposed framework outperforms the state-of-the-art online distillation methods by a large margin, and shows its efficacy in learning collaboratively between ViT-based and CNN-based models.