In this paper, we derive a large deviation principle for a stochastic 2D Allen-Cahn-Navier-Stokes system with a multiplicative noise of Lévy type. The model consists of the Navier-Stokes equations for the velocity, coupled with a Allen-Cahn system for the order (phase) parameter. The proof is based on the weak convergence method introduced in [A. Budhiraja, P. Dupuis and V. Maroulas, Variational representations for continuous time processes, Ann. Inst. Henri Poincar Probab. Stat. 47(3) (2011) 725747].