Conventional topic models are ineffective for topic extraction from microblog messages, because the data sparseness exhibited in short messages lacking structure and contexts results in poor message-level word co-occurrence patterns. To address this issue, we organize microblog messages as conversation trees based on their reposting and replying relations, and propose an unsupervised model that jointly learns word distributions to represent: (1) different roles of conversational discourse, and (2) various latent topics in reflecting content information. By explicitly distinguishing the probabilities of messages with varying discourse roles in containing topical words, our model is able to discover clusters of discourse words that are indicative of topical content. In an automatic evaluation on large-scale microblog corpora, our joint model yields topics with better coherence scores than competitive topic models from previous studies. Qualitative analysis on model outputs indicates that our model induces meaningful representations for both discourse and topics. We further present an empirical study on microblog summarization based on the outputs of our joint model. The results show that the jointly modeled discourse and topic representations can effectively indicate summary-worthy content in microblog conversations.