In this work, we propose a novel two-stage framework named FaceInpainter to implement controllable Identity-Guided Face Inpainting (IGFI) under heterogeneous domains. Concretely, by explicitly disentangling foreground and background of the target face, the first stage focuses on adaptive face fitting to the fixed background via a Styled Face Inpainting Network (SFI-Net), with 3D priors and texture code of the target, as well as identity factor of the source face. It is challenging to deal with the inconsistency between the new identity of the source and the original background of the target, concerning the face shape and appearance on the fused boundary. The second stage consists of a Joint Refinement Network (JR-Net) to refine the swapped face. It leverages AdaIN considering identity and multi-scale texture codes, for feature transformation of the decoded face from SFI-Net with facial occlusions. We adopt the contextual loss to implicitly preserve the attributes, encouraging face deformation and fewer texture distortions. Experimental results demonstrate that our approach handles high-quality identity adaptation to heterogeneous domains, exhibiting the competitive performance compared with state-of-the-art methods concerning both attribute and identity fidelity.