Caregiving for children with autism spectrum disorder (ASD) poses significant stress for parents, necessitating an exploration of mitigating factors. This study investigates the interplay between Family Sense of Coherence, Psychological Capital and caregiver stress in this context. A total of 205 caregivers of children with ASD participated in this cross-sectional study. Data were collected on Family Sense of coherence, Psychological Capital (encompassing hope, resilience, optimism and self-efficacy) and caregiver stress. Structural equation modelling was employed to test the mediation effect of psychological capital between family sense of coherence and caregiver stress. The results indicated a strong positive correlation between family sense of coherence and all subdomains of psychological capital, with coefficients ranging from 0.541 to 0.610. Conversely, psychological capital demonstrated significant negative correlations with various domains of the Kingstone Caregiver Stress Scale, including caregiving, family issues and financial issues (coefficients from −0.443 to −0.427). Furthermore, family sense of coherence showed a direct negative effect on stress (β = −0.384, p < 0.001). Notably, the study revealed a significant mediating role of psychological capital in the relationship between family sense of coherence and caregiver stress, with an indirect effect of family sense of coherence on stress through psychological capital (β = −0.127). The findings underscore the crucial role of family sense of coherence and psychological capital in enhancing psychological resources and mitigating stress among caregivers of children with ASD. These results suggest that interventions aimed at strengthening family coherence and building psychological capital could be effective strategies in alleviating stress among caregivers of children with ASD. Healthcare professionals should consider incorporating family coherence approaches and psychological capital techniques in their support programs for these caregivers.