Background: The double role of caregiver-employee (CE) defines those workers who simultaneously serve as an informal, unpaid care provider for sick, disabled, or elderly relatives, and it is a situation that is on the increase in most western countries. Providing informal caregiving can lead to detrimental effects on emotional well-being and several physical and psychological diseases (e.g., caregiver-burden). CEs can suffer double discomfort (at work and at home), but, first of all, they can be exposed to a high level of home-to-work conflict (HWI). In this study, we analyzed the CE phenomenon in a typical Italian public company, where the mean age of workers is particularly high. Methods: An online questionnaire related to the perception of HWI, well-being, and discomfort at work (depression, emotional exhaustion, job engagement) in relation to the family load (none, parents with <12 children to care for, caregiver to other adults, or children and older adults to care for/old/children to care for employees) was answered by 1704 administrative workers. Results: More than 20% of our sample was included in the elder caregiver condition or in the double role or “sandwiched” condition with older adults and children to care for. The family load changed significantly between the different age groups: for workers aged between 55 and 64 years, the percentage was nearly 27%. CEs had higher levels of HWI and of personal and job discomfort and lower levels of engagement, when compared with non-CEs. Having “only” older adults to care for (the typical CE condition) was associated with having the most negative results. Conclusion: This study confirms and underlines the increasing number of CEs in western organizations and their higher levels of HWI, work disengagement, emotional exhaustion, and depression. As the general population and workforce experience increased “graying,” and many more workers become CEs out of necessity, stable caregiver-friendly workplace policies (CFWPs) should be developed.