Structured language models for speech recognition have been shown to remedy the weaknesses of n-gram models. All current structured language models are, however, limited in that they do not take into account dependencies between non-headwords. We show that non-headword dependencies contribute to significantly improved word error rate, and that a data-oriented parsing model trained on semantically and syntactically annotated data can exploit these dependencies. This paper also contains the first DOP model trained by means of a maximum likelihood reestimation procedure, which solves some of the theoretical shortcomings of previous DOP models.