Despite its success in self-supervised learning, contrastive learning is less studied in the supervised setting. In this work, we first use a set of pilot experiments to show that in the supervised setting, the cross-entropy loss objective (CE) and the contrastive learning objective often conflict with each other, thus hindering the applications of CL in supervised settings. To resolve this problem, we introduce a novel \underline{A}ligned \underline{C}ontrastive \underline{L}earning (ACL) framework. First, ACL-Embed regards label embeddings as extra augmented samples with different labels and employs contrastive learning to align the label embeddings with its samples' representations. Second, to facilitate the optimization of ACL-Embed objective combined with the CE loss, we propose ACL-Grad, which will discard the ACL-Embed term if the two objectives are in conflict. To further enhance the performances of intermediate exits of multi-exit BERT, we further propose cross-layer ACL (ACL-CL), which is to ask the teacher exit to guide the optimization of student shallow exits. Extensive experiments on the GLUE benchmark results in the following takeaways: (a) ACL-BRT outperforms or performs comparably with CE and CE+SCL on the GLUE tasks; (b) ACL, especially CL-ACL, significantly surpasses the baseline methods on the fine-tuning of multi-exit BERT, thus providing better quality-speed tradeoffs for low-latency applications.