The observed orbital characteristics of post-asymptotic giant branch (post-AGB) and post-red giant branch (post-RGB) binaries are not understood. We suspect that the missing ingredients to explain them probably lie in the continuous interaction of the central binary with its circumstellar environment. We aim at studying the circumbinary material in these complex systems by investigating the connection between the innermost and large-scale structures. We perform high-angular resolution observations in the near-infrared continuum of HD101584, which has a complex structure as seen at millimeter wavelengths with a disk-like morphology and a bipolar outflow due to an episode of strong binary interaction. To account for the complexity of the target we first perform an image reconstruction and use this result to fit a geometrical model to extract the morphological and thermal features of the environment. The image reveals an unexpected double-ring structure. We interpret the inner ring to be produced by emission from dust located in the plane of the disk and the outer ring to be produced by emission from dust that is located 1.6[D/1kpc] au above the disk plane. The inner ring diameter (3.94[D/1kpc] au), and temperature (T=1540+/-10K) are compatible with the dust sublimation front of the disk. The origin of the out-of-plane ring (with a diameter of 7.39[D/1kpc] au and a temperature of 1014+/-10K) could be due to episodic ejection or a dust condensation front in the outflow. The observed outer ring is possibly linked with the blue-shifted side of the large scale outflow seen by ALMA and is tracing its launching location to the central star. Such observations give morphological constraints on the ejection mechanism. Additional observations are needed to constrain the origin of the out-of-plane structure.