International research has underlined that both interpersonal, self-regulation, and comorbid variables can lead to a higher risk of developing internet addiction (IA) among young adults. To date, no studies have explored the interplay between young adults’ family functioning, impulsivity, and psychopathological difficulties. In a community sample of 244 young adult university students, this study aims to assess the relationship between young adults’ IA and young adults’ gender, the perception of their family functioning, impulsivity level, and depressive and anxiety symptoms, considering the possible interplay between these variables. The presence and the severity of IA were addressed through the Internet Addiction Test (IAT). Moreover, young adults filled out self-reporting questionnaires, assessing their perception of family functioning and their impulsivity levels and psychopathological symptoms. Results showed no significant association between the youth’s gender and IA. However, moderately addicted young adults were more likely to report poorer quality of family affective involvement and higher attentional impulsivity and depressive problems than other groups. Moreover, young adults’ attentional impulsivity mediated the relationship between family affective involvement and IA. This study provides new evidence on the complex interaction between individuals and interpersonal risk factors involved in IA among young adults, with important implications for the planning of intervention treatments.