  Motivated by the fact that many bilayer quantum magnets occur in nature, we
generalize the study of thermal Hall transports of spin excitations to bilayer
magnetic systems. It is shown that bilayer magnetic systems can be coupled
either ferromagnetically or antiferromagnetically. We study both scenarios on
the honeycomb lattice and show that the system realizes topologically
nontrivial magnon bands induced by alternating next-nearest-neighbour
Dzyaloshinsky-Moriya interaction (DMI). As a result, the bilayer system
realizes both magnon Hall effect and magnon spin Nernst effect. We show that
antiferromagnetically coupled layers differ from ferromagnetically coupled
layers by a sign change in the conductivities as the magnetic field is
reversed. Furthermore, Chern number protected magnon edge states are observed
and propagate in the same direction on the top and bottom layers in
ferromagnetically coupled layers, whereas the magnon edge states propagate in
opposite directions for antiferromagnetically coupled layers.
