We present a probabilistic model extension to the Tesnie`re Dependency Structure (TDS) framework formulated in (Sangati and Mazza, 2009). This representation incorporates aspects from both constituency and dependency theory. In addition, it makes use of junction structures to handle coordination constructions. We test our model on parsing the English Penn WSJ treebank using a re-ranking framework. This technique allows us to efficiently test our model without needing a specialized parser, and to use the standard evaluation metric on the original Phrase Structure version of the treebank. We obtain encouraging results: we achieve a small improvement over state-of-the-art results when re-ranking a small number of candidate structures, on all the evaluation metrics except for chunking.