In this paper we examine how traditional views of normality are negotiated, indorsed and resisted when talking about children with heart defects. Having as a starting point an ethnographic project that aimed to study knowledge construction when being pregnant or having a child with a heart defect, we focus on argumentation put forward by clinicians and parents in order to understand the forms that normality takes in relation to children's health and illness and the way that it is constructed argumentatively and linguistically. More specifically, we draw data from recorded doctor-patient consultations, ethnographic interviews and entries from family blogs and forums and focus on those instances where normality is negotiated as a means of providing a medical consultation or of taking and motivating decisions about the child's health and everyday life. The analysis is conducted by identifying content and logical topics in the data and showing how constructions of normality and alternative conceptions are constructed in discourse. Discourses are additionally related to discursive, semiotic framing and the realization of norms. Our results highlight a duality that is being painted both in the clinicians and in the parents' discourse when negotiating the illness and the accompanying risks in the child's everyday life. Some of the traditional norms being re-constructed and re-negotiated in the data are those of stigmatization, diversity, responsibility and freedom of choice.