Efficiently mapping multiple virtual infrastructures (VIs) onto the same physical substrate with survivability is one of the fundamental challenges related to network virtualization in transport software-defined networks (T-SDNs). In this paper, we study the survivable VI mapping problem in T-SDNs with the objective of minimizing the VI request blocking probability. In particular, we address the subproblems of modulation selection and spectrum allocation in the process of provisioning optical channels to support virtual links, taking into consideration the optical layer constraints such as the transmission reach constraint and the spectral continuity constraint. We propose an auxiliary-graph-based algorithm, namely, parallel VI mapping (PAR), to offer dedicated protection against any single physical node or link failure. More specifically, the PAR algorithm can jointly optimize the assignments of mapping the primary and backup VIs by adopting the modified Suurballe algorithm to find the shortest pair of node-disjoint paths for each virtual link. Through extensive simulations, we demonstrate that the PAR algorithm can significantly reduce the VI request blocking probability and improve the traffic-carrying capacity of the networks, compared to the baseline sequential VI mapping approaches.