This paper discusses the coupling and interaction of a classical continuum model with another continuum model with random parameters. The former model, deterministic, aims at representing a part of the domain where the local fluctuations of the parameters, such as Young’s modulus, do not influence the output of interest in a significant manner, and where a homogenized model is sufficient to predict this output. The latter model, stochastic, stands for the part of the domain where the local behavior is of interest and the fluctuations of the parameters cannot be considered only in a homogenized way. The coupling of these models is performed in the Arlequin framework. This paper focuses on the technical definitions of the spaces and operators introduced in the Arlequin framework for that particular problem, and on the definition of the corresponding discretized formulations. A simple example is shown, emphasizing the gain in computational power to compute the mean and confidence intervals in the region of interest.