Users often access and re-access more than one site during an online session, effectively engaging in multitasking. In this paper, we study the effect of online multitasking on two widely used engagement metrics designed to capture users browsing behavior with a site. Our study is based on browsing data of 2.5M users across 760 sites encompassing diverse types of services such as social media, news and mail. To account for multitasking we need to redefine how user sessions are represented and we need to adapt the metrics under study. We introduce a new representation of user sessions: tree-streams - as opposed to the commonly used click-streams - present a more accurate picture of the browsing behavior of a user that includes how users switch between sites (e.g., hyperlinking, teleporting, backpaging). We then discuss a number of insights on multitasking patterns, and show how these help to better understand how users engage with sites. Finally, we define metrics that characterize multitasking during online sessions and show how they provide additional insights to standard engagement metrics.