Meme captioning, the task of generating a sentence that describes the meaning of a meme, is both challenging and important in advancing Computational Meme Understanding (CMU). However, existing research has not explored its decomposition into subtasks or its connections to other CMU tasks. To address this gap, we introduce MemeInterpret, a meme corpus containing meme captions together with corresponding surface messages and relevant background knowledge. Strategically built upon the Facebook Hateful Memes dataset, MemeInterpret is the last piece in a set of corpora that unifies three major categories of CMU tasks for the first time. Extensive experiments on MemeInterpret and connected datasets suggest strong relationships between meme captioning, its two proposed subtasks, and the other two key categories of CMU tasks: classification and explanation. To stimulate further research on CMU, we make our dataset publicly available at https://github.com/npnkhoi/MemeInterpret.