In millimeter wave (mmW) networks, for example 60 GHz networks, nodes in the network have to use directional antennas to communicate with each other to overcome high propagation losses and achieve high data rates. The narrow main beam widths of directional antennas also provide several benefits such as high gain and high spatial reuse. In this paper, we propose a dynamic node-disjoint multipath routing protocol for 60 GHz networks to improve the capacity of the network by utilizing the benefit of directional antennas. We propose three Route Request broadcasting schemes and three Route Request forwarding schemes in the route discovery stage along with a greedy node-disjoint path selection algorithm. The performance of each proposed scheme is evaluated using the ns-2 simulator. Simulation results demonstrate that by using appropriate Route Request broadcasting and forwarding schemes, node-disjoint paths can be found for each pair of source and destination. By using these node-disjoint paths, the aggregated throughput of the network is higher on average when there are one or more TCP flows in the network.