Co-viewing video lectures, where students watch lectures simultaneously with one or more remote peers and engage in interpersonal communication on learning tasks online, is becoming increasingly popular. However, there is a dearth of studies examining students' behavioral and cognitive patterns during the co-viewing process. This study employed eye-tracking and screen recording methods to examine undergraduate students' learning processes in co-viewing video lectures. It specifically focused on how students used video lectures and engaged in discussions to complete a design task. Lag sequential analysis of learning behaviors revealed that, compared to low-performers, high-performers were more engaged in behavioral sequences involving clarifying learning tasks. Furthermore, epistemic network analysis of conversations revealed that high-performers demonstrated stronger connections between deep-level knowledge and a high level of uptake in design skills. In contrast, low-performers exhibited more connections between superficial-level knowledge and a low level of uptake in these skills. The findings suggest that in co-viewing video lectures, it's crucial to engage students in clarifying behavioral sequences. Furthermore, the co-occurrence of deep-level knowledge, design skills, and a high level of uptake in shared ideas significantly enhances learning. Our research on learning processes suggests important strategies for students during co-viewing of video lectures: teachers are encouraged to design effective interactive activities and create suitable support interventions to enhance student learning performance in video lectures.