We address the problem of joint path selection and rate allocation in multipath streaming in order to optimize a media specific quality of service. An optimization problem is proposed, which aims at minimizing a video distortion metric based on sequence-dependent parameters, and transmission channel characteristics, for a given network infrastructure. Even if in general, optimal path selection and rate allocation is an NP complete problem, an in-depth analysis of the media distortion evolution allows to define a low complexity algorithm for an optimal streaming strategy. In particular, we show that a greedy allocation of rate along paths with increasing error probability leads to an optimal solution. We argue that a network path shall not be chosen for transmission, unless all other available paths with lower error probability have been chosen. Moreover, the chosen paths should be used at their maximum available end-to-end bandwidth. Simulation results show that the optimal rate allocation carefully trades off total encoding/transmission rate, with the end-to-end transmission error probability and the number of chosen paths. In many cases, the optimal rate allocation provides more than 20% improvement in received video quality, compared to heuristic-based algorithms. This motivates its use in multipath networks, where it optimizes media specific quality of service, and simultaneously saves network resources, with very low computational complexity.