Unequal error/erasure protection (UEP) is often employed in multilayer video streaming to ensure successful reception of the important reference layers. In this paper, we investigate possible ways to provide such protection to the multicasting sessions of scalable video codes (SVC) using randomized linear network codes (RLNCs). We surmised that it takes both proper combination of transmitted symbols at the source nodes and selective mixing of these symbols over the transport network to produce desirable UEP effects. To test our hypothesis, we conducted multicasting experiments over acyclic transport networks exhibiting localized or widespread packet losses. We observed that only a small collection of RLNCs is capable of providing proper UEP by taking into account the utility values of different SVC layers and the packet loss rates along different communication links. Specifically, we discovered layered coding structures in the optimal UEP-RLNCs that mirror corresponding layered structures in the scalable video codes. We also quantified the UEP capability of network codes using separation vectors and showed the gradual changes of codeword separations among different UEP-RLNCs. Finally, we developed a prototype implementation of UEP-RLNCs by extending Chou et al.'s practical network coding scheme.