Background/Objectives: Family caregivers of individuals with dementia frequently experience substantial psychological distress, yet their emotional responses are heterogeneous. Depression, anxiety and psychological well-being may co-occur in distinct patterns, and socio-economic resources such as education and income are often hypothesized to buffer caregiver distress. This study aimed to identify latent psychological profiles among dementia caregivers and to examine whether education and income moderate the association between affective symptoms and well-being. Methods: A cross-sectional study was conducted with 73 family caregivers of dementia patients attending the Neurology–Psychiatry Department of C.F.2 Clinical Hospital, Bucharest (November 2023–April 2024). Participants completed the PHQ-9 (depression), the COVI Anxiety Scale and Ryff’s Psychological Well-Being Scales. Care recipients’ cognitive status was extracted from medical records using the MMSE. Gaussian Mixture Modeling was used for latent profile analysis (LPA). Between-profile differences were examined using one-way ANOVAs and Tukey post-hoc tests. Pearson correlations assessed relationships between affective symptoms and well-being, and moderation analyses tested education and income as potential buffers. Results: LPA supported a three-profile solution: (1) low depressive symptoms with moderate anxiety (33%), (2) severe combined depression and anxiety (18%) and (3) moderately severe depression with severe anxiety (49%). Group differences were large for both depression (F(2,70) = 36.16, p < .001, η² = .68) and anxiety (F(2,70) = 73.33, p < .001, η² = .81). Caregivers in Profile 3 reported significantly higher overall well-being than those in Profile 1. Depression correlated weakly but significantly with lower autonomy (r = .24, p = .044) and self-acceptance (r = .25, p = .033), whereas anxiety showed no meaningful associations with well-being. Education and income did not moderate the relationships between affective symptoms and well-being. Conclusions: Dementia caregivers exhibit three distinct psychological profiles, reflecting heterogeneous affective responses rather than uniform distress patterns. Socio-economic resources did not significantly buffer the impact of depressive or anxiety symptoms on well-being, although higher education showed a positive association with overall well-being. These findings underscore the need for individualized screening and tailored psychological interventions to support caregiver mental health.