Background and Objectives: We examined how health-related quality of life (HRQoL) in children with congenital heart disease (CHD) and caregiver stress/burnout relate in terms of lesion severity. Methods: We enrolled 72 child–caregiver dyads at a tertiary centre (May 2023–April 2025). Children completed PedsQL and CDI (anxiety assessment via SCARED-C was descriptive and not modelled in APIM); caregivers completed SF-36, PSS-10, and the Parental Burnout Assessment (PBA). Lesion severity (mild n = 22, moderate n = 34, severe n = 16) and LVEF were abstracted. Pearson correlations and actor–partner interdependence models (APIM) estimated within- and cross-partner effects. Results: Child PedsQL decreased with severity (mild 81.2 ± 7.4; moderate 70.9 ± 8.1; severe 63.3 ± 5.1; p < 0.001); caregiver SF-36 Mental Component Summary (MCS) showed a parallel gradient (66.8 ± 9.2; 59.7 ± 8.5; 54.1 ± 7.9; p < 0.001). Child HRQoL correlated with caregiver MCS (r = 0.46) and inversely with caregiver stress (PSS r = −0.42) and burnout (PBA r = −0.39). In APIM, caregiver stress predicted a caregiver’s own MCS (actor β = −0.38, p < 0.001) and the child’s PedsQL (partner β = −0.26, p = 0.002); higher child depressive symptoms predicted lower caregiver MCS (partner β = −0.22, p = 0.006). Each step up in lesion severity independently reduced child PedsQL by 7.9 points and caregiver MCS by 5.3 points (both p < 0.001). Dyads with unscheduled hospitalizations (n = 43) had poorer scores in both members. Conclusions: Psychological wellbeing in CHD dyads is strongly interdependent; caregiver stress relates to lower child HRQoL and child mood to caregiver mental health. Brief dyadic screening (PedsQL/SF-36 with PSS/CDI) and integrated, family-focused interventions may better target high-risk families, particularly with severe lesions or recent hospitalizations.