Data publishing methods can provide available information for analysis while preserving privacy. The multiple sensitive attributes data publishing, which preserves the relationship between sensitive attributes, may keep many records from being grouped and bring in a high record suppression ratio. Another category of multiple sensitive attributes data publishing, which reduces the possibility of record suppression by breaking the relationship between sensitive attributes, cannot provide the sensitive attributes association for analysis. Hence, the existing multiple sensitive attributes data publishing fails to fully account for the comprehensive information utility. To acquire a guaranteed information utility, this article defines comprehensive information loss that considers both the suppression of records and the relationship between sensitive attributes. A heuristic method is leveraged to discover the optimal anonymity scheme that has the lowest comprehensive information loss. The experimental results verify the practice of the proposed data publishing method with multiple sensitive attributes. The proposed method can guarantee information utility when compared with previous ones.