In this work we study the existence of multiple-layered solutions to the elliptic Allen-Cahn equation in hyperbolic space. More precisely, we consider the equation −∆_H (u) + W'(u) = 0 (1), where ∆_H is the Laplace-Beltrami operator in hyperbolic space and W is a positive potential with two minima. We prove that for any given collection of non-intersecting hyperplanes in H there is a solution to (1) that has these hyperplanes as interfaces. Our result provides a Riemannian generalization of the work of M. del Pino, M. Kowalczyk, F. Pacard and J. Wei.