Hydraulic head response to stream-stage variations can be used to explore the hydraulic properties of stream-aquifer systems at a relatively large scale. These stream-stage response tests, also called flooding tests, are typically interpreted using one- or two-dimensional models that assume flow perpendicular to the river. Therefore, they cannot be applied to systems that are both horizontally and vertically heterogeneous. In this work, we use the geostatistical inverse problem to jointly interpret data from stream-stage response and pumping tests. The latter tests provide flow data (which are needed to resolve aquifer diffusivity into transmissivity and storage coefficient) and may supply supplementary small-scale information. Here, we summarize the methodology for the design, execution, and joint numerical interpretation of these tests. Application to the Aznalcóllar case study allows us to demonstrate that the proposed methodology may help in responding to questions such as the continuity of aquitards, the role and continuity of highly permeable paleochannels, or the time evolution of stream-aquifer interaction. These results expand the applicability and scope of stream-stage response tests.