BACKGROUND AND OBJECTIVE: Multi-target domain adaptation (MTDA) is a well-established technology for unsupervised segmentation. It can significantly reduce the workload of large-scale data annotations, but assumes that each domain data can be freely accessed. However, data privacy limit its deployment in real-world medical scenes. Aiming at this problem, federated learning (FL) commits a paradigm to handle private cross-institution data. METHODS: This paper makes the first attempt to apply FedMTDA to medical image segmentation by proposing a personalized Federated Bi-pole Collaborative Calibration (pFedBCC) framework, which leverages unannotated private client data and a public source-domain model to learn a global model at the central server for unsupervised multi-type immunohistochemically (IHC) image segmentation. Concretely, pFedBCC tackles two significant challenges in FedMTDA including client-side prediction drift and server-side aggregation drift via Semantic-affinity-driven Personalized Label Calibration (SPLC) and Source-knowledge-oriented Consistent Gradient Calibration (SCGC). To alleviate local prediction drift, SPLC personalizes a cross-domain graph reasoning module for each client, which achieves semantic-affinity alignment between high-level source- and target-domain features to produce pseudo labels that are semantically consistent with source-domain labels to guide client training. To further alleviate global aggregation drift, SCGC develops a new conflict-gradient clipping scheme, which takes the source-domain gradient as a guidance to ensure that all clients update with similar gradient directions and magnitudes, thereby improving the generalization of the global model. RESULTS: pFedBCC is evaluated on private and public IHC benchmarks, including the proposed MT-IHC dataset, and the panCK, BCData, DLBC-Morph and LYON19 datasets. Overall, pFedBCC achieves the best performance of 88.8% PA on MT-IHC, as well as 88.4% PA on the LYON19 dataset, respectively. CONCLUSIONS: The proposed pFedBCC performs better than all comparison methods. The ablation study also confirms the contribution of SPLC and SCGC for unsupervised multi-type IHC image segmentation. This paper constructs a MT-IHC dataset containing more than 19,000 IHC images of 10 types (CgA, CK, Syn, CD, Ki67, P40, P53, EMA, TdT and BCL). Extensive experiments on the MT-IHC and public IHC datasets confirm that pFedBCC outperforms existing FL and DA methods.