Domain adaptation using graph networks learns label-discriminative and network-invariant node embeddings by sharing graph parameters. Most existing works focus on domain adaptation of homogeneous networks. The few works that study heterogeneous cases only consider shared node types but ignore private node types in individual networks. However, for given source and target heterogeneous networks, they generally contain shared and private node types, where private types bring an extra challenge for graph domain adaptation. In this paper, we investigate Heterogeneous Information Networks (HINs) with partially shared node types and propose a novel Domain Adaptive Heterogeneous Graph Transformer (DA-HGT) to handle the domain shift between them. DA-HGT can not only align the distribution of identical-type nodes and edges in two HINs but also make full use of different-type nodes and edges to improve the performance of knowledge transfer. Extensive experiments on several datasets demonstrate that DA-HGT can outperform state-of-the-art methods in various domain adaptation tasks across heterogeneous networks.