Background: Influential philosophers have suggested that interdisciplinarity is crucial for ecosystem management and scientific practice, and for education to democracy. However, a historical review of the rise of disciplines points at their compartmentalization in schools. An analysis of "core construct categories" of three disciplines, shows that this compartmentalization may decrease when dialogic argumentation is enacted. This background led us to launch an interdisciplinary program in schools. In previous publications, we identified multiple constraints in its implementation and listed design principles for affording interdisciplinary dialogic argumentation. Method: We adopt a "narrative approach" to analyze classroom talk, and ask whether and how interdisciplinary processes emerge in this talk. Findings: Students maintain dialogic argumentation around Interdisciplinary Social Dilemmas, but guidance is necessary for integrating knowledge from different disciplines. When the teacher is attentive to student's unarticulated references to disciplinary ideas, she may subtly guide the emergence of interdisciplinary dialogic argumentation. Often, the teacher misses those opportunities and declaims the integration of knowledge in a non-dialogic talk. Contribution: Dialogic Education is crucial for the success of interdisciplinary programs in schools, but the actual emergence of interdisciplinary processes depends on the handling of organizational and institutional constraints, on huge design efforts, and on subtle guidance.