Two aspects that characterize the Mediterranean diet (MD) are “what” and “how” we eat. Conviviality relates to “how” we eat and to the pleasure of sharing meals with significant people. The most studied concept is “family meals”, which includes conviviality, which involves “enjoying” family meals. Given the lack of research on convivial family meals in Mediterranean countries, the purpose of this qualitative study was to analyze the family meal representations and practices of families with 12- to 16-year-old adolescents to assess whether they responded to a pattern of conviviality, and to examine their association with MD adherence. Twelve semi-structured interviews were conducted and food frequency and family meal questionnaires were administered. A food pattern analysis was carried out and digital photos of meals were analyzed to examine eating habits and meal composition, respectively. The findings showed that parents believed family meals are a space for socialization and communication. Items relating to the conviviality of family meals identified in the study were meal frequency, meals at the table, lack of digital distractions, pleasant conversations, and time spent on family meals. Attention should be paid to conviviality in Mediterranean families when designing multi-approach strategies to promote healthy eating among adolescents.