The changes deriving from the birth of a child with a congenital anomaly (CA) or cerebral palsy (CP) imply, in many cases, an increased interaction with health services. A cross-sectional descriptive study was conducted with a convenience sample of parents of children diagnosed with four groups of CA (severe heart anomalies, spina bifida, orofacial clefts, and Down syndrome) and/or CP. A semistructured online questionnaire to be answered by parents was sent by web link to focal points of five parent associations and professional institutions. Data were analyzed through thematic content analysis (open-ended questions) and descriptive analysis (closed-ended questions). The results indicate consistency of responses of parents of children diagnosed with different conditions, namely with respect to the perception of health services and professionals. Closed and open-ended responses indicated three main topics in the interaction between health services and parenthood: information, coordinated and integrated responses, and support. The less positive outcomes suggest unmet information needs, while positive aspects include confidence in the care provided and the “training” received from health professionals.