Sparse aperture masking interferometry (SAM) is a high-resolution observing technique, used in the optical and infrared, that allows for imaging at and beyond a telescope's diffraction limit. The technique is ideal for searching for stellar companions at small separations from their host star; however, previous analyses of SAM observations of the young stars which are surrounded by dusty disks have had difficulties disentangling planet and extended disk emission. We present a new analysis of VLT/SPHERE-IRDIS SAM data of the transition disks LkCa 15 and HD 100546. We use a new approach to the problem of disentangling point source emission from extended disk emission, fitting geometrical disk and planet models to the data and optimizing via nested sampling. We report detections of previously known extended disk structure in both LkCa 15 and HD 100546, as well as limits on companion candidates within these disks. We also present a preliminary analysis of JWST NIRISS Aperture Masking Interferometry data for PDS 70, HD 135344B and HD 100546.