For many music analysis problems, we need to know the presence of instruments for each time frame in a multi-instrument musical piece. However, such a frame-level instrument recognition task remains difficult, mainly due to the lack of labeled datasets. To address this issue, we present in this paper a large-scale dataset that contains synthetic polyphonic music with frame-level pitch and instrument labels. Moreover, we propose a simple yet novel network architecture to jointly predict the pitch and instrument for each frame. With this multitask learning method, the pitch information can be leveraged to predict the instruments, and also the other way around. And, by using the so-called pianoroll representation of music as the main target output of the model, our model also predicts the instruments that play each individual note event. We validate the effectiveness of the proposed method for framelevel instrument recognition by comparing it with its singletask ablated versions and three state-of-the-art methods. We also demonstrate the result of the proposed method for multipitch streaming with real-world music. For reproducibility, we will share the code to crawl the data and to implement the proposed model at: https://github.com/biboamy/ instrument-streaming.