Unsupervised constituency parsers organize phrases within a sentence into a tree-shaped syntactic constituent structure that reflects the organization of sentence semantics. However, the traditional objective of maximizing sentence log-likelihood (LL) does not explicitly account for the close relationship between the constituent structure and the semantics, resulting in a weak correlation between LL values and parsing accuracy. In this paper, we introduce a novel objective that trains parsers by maximizing SemInfo, the semantic information encoded in constituent structures. We introduce a bag-of-substrings model to represent the semantics and estimate the SemInfo value using the probability-weighted information metric. We apply the SemInfo maximization objective to training Probabilistic Context-Free Grammar (PCFG) parsers and develop a Tree Conditional Random Field (TreeCRF)-based model to facilitate the training. Experiments show that SemInfo correlates more strongly with parsing accuracy than LL, establishing SemInfo as a better unsupervised parsing objective. As a result, our algorithm significantly improves parsing accuracy by an average of 7.85 sentence-F1 scores across five PCFG variants and in four languages, achieving state-of-the-art level results in three of the four languages.