Sarcasm is a sophisticated speech act that is intended to express contempt or ridicule on social communities such as Twitter. In recent years, the prevalence of sarcasm on the social media has become highly disruptive to sentiment analysis systems due to not only its tendency of polarity flipping but also usage of figurative language. It is observed that sarcastic texts often convey a humorous effect. Thus, determining the humor in texts can be pertinent to the successful detection of sarcasm, and vice versa. However, current works always regard sarcasm detection and humor identification as separate tasks. In this paper, we argue that these tasks should be treated as a joint, collaborative, effort, considering the semantic connections between sarcasm and humor expressed in texts. Enlightened by the multi-task learning strategy, we present a joint architecture that settles two highly pertinent tasks, sarcasm detection and humor identification. As the basic of deep neural networks, we learn both tasks jointly exploring weight sharing to capture the task-specific features for each task and task-cross features between the two tasks. Extensive experiments on real-world datasets demonstrate that our presented model consistently enhances both sarcasm detection and humor identification tasks consistently with the help of the strong semantic relationships, achieving much better performance than state-of-the-art baselines.