  We construct a new model of two-dimensional quantum spin systems that
combines intrinsic topo- logical orders and a global symmetry called flavour
symmetry. It is referred as the bilayer Doubled Semion model (bDS) and is an
instance of symmetry-enriched topological order. A honeycomb bi- layer lattice
is introduced to combine a Double Semion Topolgical Order with a global
spin-flavour symmetry to get the fractionalization of its quasiparticles. The
bDS model exhibits non-trival braid- ing self-statistics of excitations and its
dual model constitutes a Symmetry-Protected Topological Order with novel edge
states. This dual model gives rise to a bilayer Non-Trivial Paramagnet that is
invariant under the flavour symmetry and the well-known spin flip symmetry.
