There are few programs available aimed at preventing short- and long-term negative consequences after preterm birth and covering the entire care continuum. The “Transition to Home (TtH)” model is such a program, offering structured, individual support for families with preterm infants before and after hospital discharge. This study gathers and examines the parents’ views of receiving support from an interprofessional team under the TtH model of care during hospitalization and after discharge. Using a qualitative explorative design, 39 semi-structured interviews with parents were analyzed thematically. From this analysis, three main themes were identified: (1) TtH and the relevance of continuity of care; (2) Enhancement of parents’ autonomy and self-confidence; (3) Perception of interprofessional collaboration. Within these themes, the most relevant aspects identified were continuity of care and the appointment of a designated health care professional to anchor the entire care continuum. Emotional support complemented by non-medical approaches, along with strength-based and family resource-oriented communication, also emerged as key aspects. Continuous, family-centered care and well-organized interprofessional collaboration promote the well-being of the family after a premature birth. If the aspects identified in this study are applied, the transition from hospital to home will be smoothened for the benefit of affected families.