Collaborative problem-solving (CPS) involves the interaction and interdependence of students' social and cognitive skills, making it a complex learning process. To delve into the complex dynamics of CPS, previous research has categorized socio-cognitive roles, providing insights into social-cognitive frameworks. However, despite the specific cognitive and social interaction structures employed by roles to engage in CPS interactions, most existing research primarily focuses on individual roles, neglecting inter-role interactions. To fill this gap, twelve triad groups were formed by engaging 36 undergraduate students in online CPS activities to examine differences in social and cognitive interaction structures across different roles and group compositions. Additionally, analyze the differences in CPS processes among various group compositions. The analyses identified five roles ("Lurkers," "Followers," "Drivers," "Influential Actors," and "Innovators") and three group compositions ("Balanced groups," "Decentralized groups," and "Power Struggle groups"). The socio-cognitive structure of Balanced groups, along with other evidence, indicates effective information sharing and negotiation interactions. In contrast, "Decentralized" and "Power Struggle groups" exhibited various deficiencies in their socio-cognitive structures, negatively impacting group collaboration processes. These insights provide educators with a comprehensive guide to fostering effective group compositions and role dynamics in online CPS settings, thereby enhancing the overall success of CPS. Additionally, possible activity design considerations and scaffolding strategies are also discussed.