Graphical models are used in many applications such as medical diagnostics and computer security. Increasingly often, the estimation of such models has to be performed on several predefined strata of the whole population. For instance, in epidemiology and clinical research, strata are often defined according to age, gender, treatment, or disease type. In this article, we propose new approaches dedicated to the estimation of binary graphical models on such strata. These approaches are implemented by combining well-known methods that have been developed in the context of a single binary graphical model, with penalties encouraging structured sparsity, which have recently been shown to be appropriate when dealing with stratified data. Empirical comparisons on synthetic data highlight that our approaches generally outperform its competitors. We present an application of the approach to study associations among the injuries suffered by victims of road accidents according to road user type.