The conflict between work and family demands increased during the COVID-19 pandemic due to changes in lifestyle related to the lockdown. This study examines the associations between work-family conflict (WFC) and family-work conflict (FWC) with work-specific, family-specific, and well-being-related variables during the second wave of the COVID-19 pandemic. The results may be used in practice to improve the well-being of employees by adjusting home-based work and family areas of life to dynamic changes during the pandemic. The sample of 736 adults from Poland (53.26%) and Ukraine (46.74%), aged between 19 and 72 (M = 39.40; SD = 10.80), participated in the study. The cross-sectional study was performed using an online survey, including sociodemographic variables, measures of WFC, time pressure, remote work assessment (RWAS), physical health (GSRH), life satisfaction (SWLS), perceived stress (PSS-10), anxiety (GAD-7), and depression (PHQ-9). This study showed numerous inter-group differences in all variables across the country, gender, relationship status, parenthood, caring for children under 12, and remote working status. A high WFC is more likely among Polish workers (than Ukrainian workers), people with a low level of self-perceived time pressure, and high symptoms of stress. Caring for children under 12, low self-perceived time pressure, and high stress can predict FWC. Various paths lead from perceived stress via WFC and FWC, physical health, anxiety, and depression to life satisfaction, as suggested by the structural equation modeling analysis. Parents of children under 12 and women are the most vulnerable groups for increased WFC, FWC, and worse mental health and well-being. Prevention programs should focus on reducing stress, anxiety, and work demands in these adult populations. A unique contribution to the existing knowledge revealed patterns of associations between WFC and FWC in relation to well-being dimensions in a cross-cultural context during the pandemic.