In this talk, I introduce a class of generalized backward doubly stochastic differential equations whose coefficient contains the subdifferential operators of two convex functions, which are also called as generalized backward doubly stochastic variational inequalities, are considered. By means of a penalization argument based on Yosida approximation, we establish the existence and uniqueness of the solution. As an application, this result is used to derive existence result of stochastic viscosity solution for a class of multivalued stochastic Dirichlet-Neumann problems.