Within the last three years, the COVID-19 pandemic outbreak has contributed to changing many aspects of individual and collective life. Focusing on professional life, the forced shift to remote working modalities, the consequent blurring of work–family (WF) boundaries, and the difficulties for parents in childrearing have significantly impacted family routines. These challenges have been more evident for some specific vulnerable categories of workers, such as dual-earner parents. Accordingly, the WF literature investigated the antecedents and outcomes of WF dynamics, highlighting positive and negative aspects of digital opportunities that may affect WF variables and their consequences on workers’ well-being. In view of the above, the present study aims to investigate the key role of WF conflict and WF balance in mediating the relationship between technostress and work exhaustion. Structural Equation Modeling (SEM) was used to examine direct and indirect relationships among technostress, WF conflict, WF balance, and work exhaustion. Respondents were 376 Italian workers, specifically dual-earner parents who have at least one child. Results and implications are discussed with specific reference to the organizational policies and interventions that could be developed to manage technostress and WF conflict, fostering individual and social adjustment to the new normal.