Online discussion forum creates an asynchronous conversation environment for online users to exchange ideas and share opinions through a unique thread-reply communication mode. Accurately modeling information dynamics under such a mode is important, as it provides a means of mining latent spread patterns and understanding user behaviors. In this paper, we design a novel temporal point process model to characterize information cascades in online discussion forums. The proposed model views the entire event space as a nested structure composed of main thread streams and their linked reply streams, and it explicitly models the correlations between these two types of streams through their intensity functions. Leveraging the Reddit data, we examine the performance of the designed model in different applications and compare it with other popular methods. The experimental results have shown that our model can produce competitive results, and it outperforms state-of-the-art methods in most cases.