Current word alignment models do not distinguish between different types of alignment links. In this paper, we provide a new probabilistic model for word alignment where word alignments are associated with linguistically motivated alignment types. We propose a novel task of joint prediction of word alignment and alignment types and propose novel semi-supervised learning algorithms for this task. We also solve a sub-task of predicting the alignment type given an aligned word pair. In our experimental results, the generative models we introduce to model alignment types significantly outperform the models without alignment types.