We present a novel approach that integrates algorithmic recommender techniques with interactive faceted filtering methods. We refer to this approach as blended recommending. It allows users to interact with a set of filter facets representing criteria that can serve as input for different recommendation methods including both collaborative and content-based filtering. Users can select filter criteria from these facets and weight them to express their preferences and to exert control over the hybrid recommendation process. In contrast to hard Boolean filtering, the method aggregates the weighted criteria and calculates a ranked list of recommendations that is visualized and immediately updated when users change the filter settings. Based on this approach, we implemented an interactive movie recommender, MyMovieMixer. In a user study, we compared the system with a conventional faceted filtering system that served as a baseline to obtain insights into user interaction behavior and to assess recommendation quality for our system. The results indicate, among other findings, a higher level of perceived user control, more detailed preference settings, and better suitability when the search goal is vague.