Both sentiment analysis and topic classification are frequently used in customer care and marketing. They can help people understand the brand perception and customer opinions from social media, such as online posts, tweets, forums, and blogs. As such, in recent years, many solutions have been proposed for both tasks. However, we believe that the following two problems have not been addressed adequately: (1) Conventional solutions usually treat the two tasks in isolation. When the two tasks are closely related (e.g., posts about "customer care" often have a "negative" tone), exploring their correlation may yield a better accuracy; (2) Each post is usually assigned with only one sentiment label and one topic label. Since social media is, compared to traditional document corpus, more noisy, ambiguous, and sparser, single label classification may not be able to capture the post classes accurately. To address these two problems, in this paper, we propose a multi-task multi-label (MTML) classification model that performs classification of both sentiments and topics concurrently. It incorporates results of each task from prior steps to promote and reinforce the other iteratively. For each task, the model is trained with multiple labels so that they can help address class ambiguity. In the empirical validation, we compare the accuracy of MTML model against four competing methods in two different settings. Results show that MTML produces a much higher accuracy of both sentiment and topic classifications.