  In this paper, we study systems of nonlinear second-order variational
inequalities with interconnected bilateral obstacles with non-local terms. They
are of min-max and max-min types and related to a multiple modes zero-sum
switching game in the jump-diffusion model. Using systems of penalized
reflected backward SDEs with jumps and unilateral interconnected obstacles, and
their associated deterministic functions, we construct for each system a
continuous viscosity solution which is unique in the class of functions with
polynomial growth.
