Are hybrid-species individuals considered to be of the same species as their parents?
TL/DR We usually don't give specific names to those hybrids. 

This is a fairly complicated question, actually, without an easy answer. Hybridization can have different outcomes, depending on how different the hybridizing species are. The cases you mention (liger, mules) actually do not deserve a specific names, because, first, they don't occur in nature, and, second, they are sterile, so there's no reproduction, hence no progeny. This lack of descendants goes against any defenition of species that we have in biology. There are cases where hybrids might become their own species, for example the butterfly Heliconius heurippa appears to be a species that evolved through hybridization between two closely related Heliconius species. There are also many examples in plants and more are being discovered in animals. These cases do receive a species name, because they occur in nature and populations can be predictably found. 

Another case, similar to the cases you mention, involve hybridizations that occur in nature, but are rare and the individual rarely has any significance effect on the population. Sometimes those individuals are fertile, but look so different that might not be able to reproduce. Other times they can only reproduce with one of the parental species and if this happens successfully, new alleles can be introgressed into the parental genome. But for what we know, reproductive barriers between species tend to be successful in nature, tend to be broken down with human intervention (captivity, movement of species, among others) and, in most cases, don't have a significant evolutionary impact, except the cases when they do.