We present in this paper well-founded cross-language extensions of the recently introduced models in the information-based family for information retrieval, namely the LL (log-logistic) and SPL (smoothed power law) models of [4]. These extensions are based on (a) a generalization of the notion of information used in the information-based family, (b) a generalization of the random variables also used in this family, and (c) the direct expansion of query terms with their translations. We then review these extensions from a theoretical point-of-view, prior to assessing them experimentally. The results of the experimental comparisons between these extensions and existing CLIR systems, on three collections and three language pairs, reveal that the cross-language extension of the LL model provides a state-of-the-art CLIR system, yielding the best performance overall.