Narrative sensemaking is an essential part of understanding sequential data. Narrative maps are a visual representation model that can assist analysts to understand narratives. In this work, we present a semantic interaction (SI) framework for narrative maps that can support analysts through their sensemaking process. In contrast to traditional SI systems which rely on dimensionality reduction and work on a projection space, our approach has an additional abstraction layer -- the structure space -- that builds upon the projection space and encodes the narrative in a discrete structure. This extra layer introduces additional challenges that must be addressed when integrating SI with the narrative extraction pipeline. We address these challenges by presenting the general concept of Mixed Multi-Model Semantic Interaction (3MSI) -- an SI pipeline, where the highest-level model corresponds to an abstract discrete structure and the lower-level models are continuous. To evaluate the performance of our 3MSI models for narrative maps, we present a quantitative simulation-based evaluation and a qualitative evaluation with case studies and expert feedback. We find that our SI system can model the analysts' intent and support incremental formalism for narrative maps.