  We present a physical scenario in which both Fermi arcs and two-dimensional
gapless Dirac states coexist as boundary modes at the same two-dimensional
surface. This situation is realized in topological insulator-Weyl semimetal
interfaces in spite of explicit time reversal symmetry breaking. Based on a
heuristic topological index, we predict that the coexistence is allowed when
(i) the corresponding states of the Weyl semimetal and topological insulator
occur at disconnected parts of the Brillouin zone separated by the Weyl nodes
and (ii) the time-reversal breaking vector defining the Weyl semimetal has no
projection parallel to the domain wall. This is corroborated by a numerical
simulation of a tight binding model. We further calculate the optical
conductivity of the coexisting interface states, which can be used to identify
them through interference experiments.
