Many real-world data can be modeled as heterogeneous graphs that contain multiple types of nodes and edges. Meanwhile, due to excellent performance, heterogeneous graph neural networks (GNNs) have received more and more attention. However, the existing work mainly focuses on the design of novel GNN models, while ignoring another important issue that also has a large impact on the model performance, namely the missing attributes of some node types. The handcrafted attribute completion requires huge expert experience and domain knowledge. Also, considering the differences in semantic characteristics between nodes, the attribute completion should be fine-grained, i.e., the attribute completion operation should be node-specific. Moreover, to improve the performance of the downstream graph learning task, attribute completion and the training of the heterogeneous GNN should be jointly optimized rather than viewed as two separate processes. To address the above challenges, we propose a differentiable attribute completion framework called AutoAC for automated completion operation search in heterogeneous GNNs. We first propose an expressive completion operation search space, including topology-dependent and topology-independent completion operations. Then, we propose a continuous relaxation schema and further propose a differentiable completion algorithm where the completion operation search is formulated as a bi-level joint optimization problem. To improve the search efficiency, we leverage two optimization techniques: discrete constraints and auxiliary unsupervised graph node clustering. Extensive experimental results on real-world datasets reveal that AutoAC outperforms the SOTA handcrafted heterogeneous GNNs and the existing attribute completion method