In this paper we introduce a joint arc-factored model for syntactic and semantic dependency parsing. The semantic role labeler predicts the full syntactic paths that connect predicates with their arguments. This process is framed as a linear assignment task, which allows to control some well-formedness constraints. For the syntactic part, we define a standard arc-factored dependency model that predicts the full syntactic tree. Finally, we employ dual decomposition techniques to produce consistent syntactic and predicate-argument structures while searching over a large space of syntactic configurations. In experiments on the CoNLL-2009 English benchmark we observe very competitive results.