Resilience literature indicates that social support is the primary external factor buffering the impact of parental psychopathology on offspring outcomes. Informal social support is particularly important in Eastern Europe owing to the limited availability of formal social support. Our study uses data from the 2019 Polish Health Interview Survey (n = 641 triads) and the method of partial least-squares path modelling to examine the intergenerational transmission of health adversities and to test the moderating effect of informal social support perceived by offspring. The path models showed significant intergenerational associations of alcohol use, tobacco smoking, and depressive symptoms, even after adjusting for socio-demographic controls. Offspring’s perceived social support strongly moderated the intergenerational association of alcohol use, meaning that those with lower perceived informal social support showed a stronger link. The Johnson–Neyman value for offspring’s perceived informal social support was approximately 0.7 standard deviations above the mean. The moderation of intergenerational associations of tobacco smoking and depressive symptoms by offspring’s perceived social support was borderline significant. The revealed deficits in informal social support for youth from families affected by alcohol use disorder should be addressed through public policy. Longitudinal studies are needed to confirm the direction of relationship between informal social support and alcohol use among Eastern European youth.