We propose a method to improve the accuracy of parsing bilingual texts (bitexts) with the help of statistical machine translation (SMT) systems. Previous bitext parsing methods use human-annotated bilingual treebanks that are hard to obtain. Instead, our approach uses an auto-generated bilingual treebank to produce bilingual constraints. However, because the auto-generated bilingual treebank contains errors, the bilingual constraints are noisy. To overcome this problem, we use large-scale unannotated data to verify the constraints and design a set of effective bilingual features for parsing models based on the verified results. The experimental results show that our new parsers significantly outperform state-of-the-art baselines. Moreover, our approach is still able to provide improvement when we use a larger monolingual treebank that results in a much stronger baseline. Especially notable is that our approach can be used in a purely monolingual setting with the help of SMT.