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In this paper, we study forward-backward doubly stochastic differentialequations driven by Brownian motions and Poisson process (FBDSDEP in short).Both the probabilistic interpretation for the solutions to a class ofquasilinear stochastic partial differential-integral equations (SPDIEs inshort) and stochastic Hamiltonian systems arising in stochastic optimal controlproblems with random jumps are treated with FBDSDEP. Under some monotonicityassumptions, the existence and uniqueness results for measurable solutions ofFBDSDEP are established via a method of continuation. Furthermore, thecontinuity and differentiability of the solutions of FBDSDEP depending onparameters is discussed. Finally, the probabilistic interpretation for thesolutions to a class of quasilinear SPDIEs is given.

Forward-Backward Doubly Stochastic Differential Equations with Random Jumps and Stochastic Partial Differential-Integral Equations