Backup paths are widely used in IP networks to protect IP links from failures. However, existing solutions such as the commonly used independent model and Shared Risk Link Group (SRLG) model do not accurately reflect the correlation between IP link failures, and thus may not choose reliable backup paths. We propose a cross-layer approach for minimizing routing disruption caused by IP link failures. We develop a probabilistically correlated failure (PCF) model to quantify the impact of IP link failure on the reliability of backup paths. With the PCF model, we propose an algorithm to choose multiple reliable backup paths to protect each IP link. When an IP link fails, its traffic is split onto multiple backup paths to ensure that the rerouted traffic load on each IP link does not exceed the usable bandwidth. We evaluate our approach using real ISP networks with both optical and IP layer topologies. Experimental results show that two backup paths are adequate for protecting a logical link. Compared with existing works, the backup paths selected by our approach are at least 18 percent more reliable and the routing disruption is reduced by at least 22 percent. Unlike prior works, the proposed approach prevents the rerouted traffic from interfering with normal traffic.