Background/Objectives: This study aims to explore family dynamics and the economic hardships experienced by families during the COVID-19 pandemic and their associations with adolescents’ health risk behaviours (HRBs). Methods: Based on a representative study of adolescents aged 11–16 conducted in Bulgaria during the COVID-19 pandemic and HBSC data from the pre-pandemic period, logistic regression models were applied, assessing cigarette smoking, vaping, alcohol use, drunkenness, and cannabis use. The independent variables included demographics, Family Affluence Scale (FAS III), family structure, ease of communication with parents, and the authors’ developed questions on parents’ income and economic status change, family conflicts, and missing contact with extended family due to the pandemic. Results: Material status of the family showed increasing differentials in adolescents’ HRBs during the pandemic. Parental unemployment, income reduction, and temporary lay-offs were associated with a higher risk of substance use. Family conflicts, missing contact with extended family, and difficulties in communication with the mother were related to a higher risk of substance use. Communication with the father was significantly associated with alcohol use and drunkenness. Boys had lower odds of vaping and higher odds of alcohol use, drunkenness, and cannabis use. Higher age and minority status were associated with an increase in adolescents’ HRBs. Conclusions: This study highlights the need for special family-focused interventions in times of health and economic crises.