The Internet topology can be viewed at the physical-, router-, PoP-, and AS-level. Intuitively, a richly connected lower level can improve the resilience of a service at higher levels. Understanding the structure of the Internet from a multilevel point of view is more realistic than examining its properties at individual levels. We have developed a framework to analyse the robustness of multilevel and multiprovider networks. We show that multilevel graphs exhibit different performance from single level graphs. Moreover, our framework validates the robustness of the Internet core due to its rich connectivity.