In cluster analysis, it could be useful to interpret the obtained partition with respect to external qualitative variables. An approach is proposed in the model-based clustering context to select a model and a number of clusters in order to get a partition which both provides a good fit with the data and is well related to the external variables. This approach makes use of the integrated joint likelihood of the data and the partitions at hand, namely the model-based partition and the partitions associated to the external variables. It is worth noticing that the known partitions are only used to select a relevant mixture model. Each mixture model is fitted by the maximum likelihood methodology from the data. Numerical experiments illustrate the promising behaviour of the derived criterion.