Ensuring secure authentication between participating entities in VANETs has emerged as a critical challenge. Most of existing schemes mainly consider authentication issue in single administrative domain and suffer from various limitations that include privacy-preserving and malicious entity tracking. This paper proposes a double-layer blockchain-assisted conditional privacy-preserving cross-domain authentication scheme (DBCPCA) that leverages blockchain technology and certificate-less signatures to address these challenges. In DBCPCA, the upper-layer blockchain is used in cross-domain authentication by sharing inter-domain information among multiple different administrative domains. The lower-layer blockchain is employed in intra-domain authentication. In DBCPCA, we also introduce an anonymity mechanism to protect the real identity of a vehicle while enabling the system to trace a malicious vehicle, thereby addressing conditional privacy-preserving concerns. In addition, a security analysis of the proposed scheme demonstrates that it can meet our specified security objectives. Finally, we make a detailed experimental comparison with the most relative solutions such as BCPPA and BCGS. The results show that the DBCPCA scheme reduces the time cost by at least 66.68 % compared to the BCPPA scheme during the signature generation phase. During the signature verification phase, the DBCPCA scheme reduces the time cost by at least 62.39 % compared to the BCGS scheme.