The popularity of HTTP-based video streaming services has been increasing in recent years. The quality of HTTP-based video streaming services is measured by the user's quality of experience (QoE). Perceptual quality (PQ), a strong indicator of the QoE, has been widely studied in the literature. Specifically, previous studies primarily focused on modeling the overall perceptual quality at the end of the viewing process. The specific influence of each event during the viewing process was neglected. Since the PQ is a function of time, which models the human perception of audiovisual services, this contribution focuses on investigating the time-varying feature of human perception. In this paper, the viewing timeline of subjects is divided into rebuffering and playback. An event-based perceptual quality assessment (EPQ) framework is introduced, which can assess the PQ of interrupted HTTP-based video streaming at any point in time. To understand the human perception of video streams with playback interruptions, a subjective quality assessment experiment was designed to obtain the PQ at a series of points in time. A between-subjects design was adopted in which each subject can view video content without repetition. Based on the experimental results, a PQ assessment model was proposed to predict the change in PQ (i.e., $\Delta$ PQ) after each rebuffering and playback. The overall PQ at any point in time is calculated as the summation of the $\Delta$ PQs of all the previous events. The experimental results demonstrated that the EPQ-based model outperforms the rebuffering components contained in the ITU-T Rec. P.1201.1, P.1201 Amd. 2 and P.1203.3 in our database.