This study aimed to explore the association between the functioning of family environment (i.e., family cohesion and family adaptability) and academic burnout of Chinese college students as well as the mediating effects of the interpersonal resource (i.e., peer support) and intrapersonal resource [i.e., positive psychological capital (PsyCap)] in this relationship. A total of 1971 Chinese undergraduates were involved in an online questionnaire survey and data analysis. It was found that family cohesion and adaptability was negatively related to academic burnout. Mediation analyses demonstrated that family cohesion and adaptability did not directly affect academic burnout, but indirectly through increasing PsyCap (characterized by optimism, hope, resilience, and self-efficacy), and through enhancing peer support and then increasing PsyCap in serial. Meanwhile, the relationship between family cohesion and adaptability and academic burnout was not mediated by peer support alone. These findings highlight the family environment’s crucial role in youth mental health and positive development in the college context.