Episodic memories reflect a bound representation of multimodal features that can be reinstated with varying levels of precision. Yet little is known about how brain networks involved in memory, including the hippocampus and posterior-medial (PM) and anterior-temporal (AT) cortical systems, functionally interact to support the quality and the content of recollection. Participants learned color, spatial, and emotion associations of objects, later reconstructing the visual features using a continuous color spectrum and 360-degree panorama scenes. Behaviorally, dependencies in memory were observed for the gist but not precision of these event associations. Supporting this integration, hippocampus, AT, and PM regions showed increased inter-network connectivity and reduced modularity during retrieval compared to encoding. These network connections, particularly to hippocampus, tracked a multidimensional, continuous measure of objective memory quality. Moreover, distinct patterns of connectivity tracked item color precision and spatial memory precision. These findings demonstrate not only how hippocampal-cortical connections reconfigure during episodic retrieval, but how such dynamic interactions might flexibly support the multidimensional quality of remembered events.