The study aimed to determine the relationship between parents’ family aspirations towards their children with disabilities and selected parental psychosocial resources, such as self-image, self-perception, perceived social support, and styles of coping with stress. The instruments included the Parental Aspirations Questionnaire by Kirenko (2012), The Tennessee Self Concept Scale by Fitts (1965), The Norbeck Social Support Questionnaire by Norbeck (1984), and Coping Inventory for Stressful Situations by Endler and Parker (1999). 361 mothers and fathers bringing up children with physical, sensory, and intellectual disabilities participated in the study. The results suggest a positive role of adaptive competences, such as adaptive coping, positive properties of self-image, as well as the negative role of maladaptive competencies such as self-criticism in mothers and fathers. Neither the positive contribution of social support nor the negative role of avoidance-oriented coping in fathers has been confirmed. Parental aspirations are part of adaptation to living with a child with a disability and will be important to support parents in recognizing the child’s potential correctly and strengthening it at all stages of development until adulthood.