(1) Background. This study assesses the quality of life in families with a member with an intellectual disability using the Family Adjustment and Adaptation Response framework. (2) Methods. The study included 515 Spanish participants whose family members with disabilities range in age from infancy to adulthood. We hypothesized that it is possible to predict parenting stress by paying attention to the meaning families give to themselves and their circumstances while controlling for the impact of other variables such as family capabilities and characteristics of the family member with disabilities. We used the Beach Center Family Quality of Life Scale and the section on Exceptional needs of medical and behavioral support from the Supports Intensity Scale, together with other potential predictors. The subscale on parental stress from the Parenting Stress Index–Short Form was utilized as a criterion measure. (3) Results. Hierarchical multiple regression analysis revealed that 49% of parental stress was predicted by dysfunctional interaction, difficult behaviors, low emotional wellbeing, poor family interaction, as well as kinship as parents, and the severity of both the medical needs and intellectual disability. (4) Conclusions. The stress experienced by those families is mostly predicted by the meaning they give to themselves and their circumstances. Implications of these findings for service delivery are discussed.