A complex system can be modeled using various fidelities with the finite element method. A high-fidelity model is expected to be more computationally expensive compared to a low-fidelity model and in general may contain more degrees of freedom and more elements. On top of this, the computational cost is expected to increase considerably if the governing equations are stochastic. This paper proposes a Bayesian multi-fidelity approach to solve stochastic boundary value problems using the finite element method. A Gaussian process metamodel is coupled with the domain decomposition method in order to solve the interface problem. Using this approach, it is possible to assimilate a low-fidelity model with a more expensive high-fidelity model. The idea is illustrated using elliptic boundary value problems.