It is shown that the matrix describing a lossless multilayer when no total reflection occurs is an element of the group SU(1,1), which is locally isomorphic to the three-dimensional Lorentz group SO(2,1). A natural identification of the reflection and transmission coefficients for the multilayer with the parameters of a Lorentz transformation is performed. The correspondence between field and space-time variables, along with the invariance of the interval, allows us to compute the invariant of the multilayer.