Most social networks can be modeled as a heterogeneous graph. Recently, advanced graph learning methods exploit the rich node properties and topological relationships for downstream tasks. That means that more private information is embedded in the representation. However, the existing privacy-preserving methods only focus on protecting the single type of node attributes or relationships, which neglect the significance of high-order semantic information. To address this issue, we propose a novel Heterogeneous graph neural network with Semantic-aware Differential privacy Guarantees named HeteSDG, which provides a double privacy guarantee and performance trade-off in terms of both graph features and topology. In particular, we first reveal the privacy leakage in heterogeneous graph and define a membership inference attack with a semantic enhancement (MIS) that will improve the means of member inference attacks by obtaining side background knowledge through semantics. Then we design a two-stage mechanism, which includes the feature attention personalized mechanism and the topology gradient perturbation mechanism, where the privacy-preserving technologies are based on differential privacy. These mechanisms will defend against MIS attacks and provide stronger interpretation, but simultaneously bring in noise for representation learning. To better balance the noise perturbation and learning performance, we utilize a bi-level optimization pattern to allocate a suitable privacy budget for the above two modules. Our experiments on four public benchmarks conduct performance experiments, ablation studies, inference attack verification, etc. The results show the privacy protection capability and generalization of HeteSDG.