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Vertical Federated Learning (VFL) enables an active party with labeled data to enhance model performance (utility) by collaborating with multiple passive parties that possess auxiliary features corresponding to the same sample identifiers (IDs). Model serving in VFL is vital for real-world, delay-sensitive applications, and it faces two major challenges: 1) robustness against arbitrarily-aligned data and stragglers; and 2) privacy protection, ensuring minimal label leakage to passive parties. Existing methods fail to transfer knowledge among parties to improve robustness in a privacy-preserving way. In this paper, we introduce a privacy-preserving knowledge transfer framework, Complementary Knowledge Distillation (CKD), designed to enhance the robustness and privacy of multi-party VFL systems. Specifically, we formulate a Complementary Label Coding (CLC) objective to encode only complementary label information of the active party's local model for passive parties to learn. Then, CKD selectively transfers the CLC-encoded complementary knowledge 1) from the passive parties to the active party, and 2) among the passive parties themselves. Experimental results on four real-world datasets demonstrate that CKD outperforms existing approaches in terms of robustness against arbitrarily-aligned data, while also minimizing label privacy leakage.