Answering database queries while preserving privacy is an important problem that has attracted considerable research attention in recent years. A canonical approach to this problem is to use synthetic data. That is, we replace the input database R with a synthetic database R* that preserves the characteristics of R, and use R* to answer queries. Existing solutions for relational data synthesis, however, either fail to provide strong privacy protection, or assume that R contains a single relation. In addition, it is challenging to extend the existing single-relation solutions to the case of multiple relations, because they are unable to model the complex correlations induced by the foreign keys. Therefore, multi-relational data synthesis with strong privacy guarantees is an open problem. In this paper, we address the above open problem by proposing PrivLava, the first solution for synthesizing relational data with foreign keys under differential privacy, a rigorous privacy framework widely adopted in both academia and industry. The key idea of PrivLava is to model the data distribution in R using graphical models, with latent variables included to capture the inter-relational correlations caused by foreign keys. We show that PrivLava supports arbitrary foreign key references that form a directed acyclic graph, and is able to tackle the common case when R contains a mixture of public and private relations. Extensive experiments on census data sets and the TPC-H benchmark demonstrate that PrivLava significantly outperforms its competitors in terms of the accuracy of aggregate queries processed on the synthetic data.