One of the main research tasks in community question answering (cQA) is finding the most relevant questions for a given new query, thereby providing useful knowledge for users. The straightforward approach is to capitalize on textual features, or a bag-of-words (BoW) representation, to conduct the matching process between queries and questions. However, these approaches have a lexical gap issue which means that, if lexicon matching fails, they cannot model the semantic meaning. In addition, latent semantic models, like latent semantic analysis (LSA), attempt to map queries to its corresponding semantically similar questions through a lower dimension representation. But alas, LSA is a shallow and linear model that cannot model highly non-linear correlations in cQA. Moreover, both BoW and semantic oriented solutions utilize a single dictionary to represent the query, question, and answer in the same feature space. However, the correlations between them, as we observe from data, imply that they lie in entirely different feature spaces. In light of these observations, this paper proposes a tri-modal deep belief network (tri-DBN) to extract a unified representation for the query, question, and answer, with the hypothesis that they locate in three different feature spaces. Besides, we compare the unified representation extracted by our model with other representations using the Yahoo! Answers queries on the dataset. Finally, Experimental results reveal that the proposed model captures semantic meaning both within and between queries, questions, and answers. In addition, the results also suggest that the joint representation extracted via the proposed method can improve the performance of cQA archives searching.