Catheter assemblies include a stabilization mechanism disposed at a distal end of the catheter assembly for stabilizing the catheter assembly within a subintimal space. The stabilization mechanism includes a self-expanding support structure that is slidably positionable within an inflatable balloon. The catheter assemblies include an outer shaft which has the balloon at a distal end thereof and an inner shaft which has the support structure mounted on a distal end thereof. The inner shaft is slidably disposed within a lumen of the outer shaft and has a first configuration in which the support structure is held in a compressed state within the outer shaft and a second configuration in which the support structure is permitted to return to an expanded state within the inflatable balloon. In the expanded state, the stabilization mechanism has a flattened laterally-extending profile.