Blockchain interoperability enables independent blockchain systems to communicate and exchange assets across heterogeneous networks. However, the lack of comprehensive security mechanisms remains a critical weakness -- one that attackers have already exploited to cause hundreds of millions of dollars in asset losses. This paper presents a systematic identification and classification of security threats facing interoperable blockchain systems, along with corresponding countermeasures for each. We organize threats into five categories: (1) core blockchain attacks, (2) network attacks, (3) interoperability-specific attacks, (4) social engineering, and (5) code vulnerabilities, with particular attention to smart contract weaknesses. For each identified threat, we analyze its attack surface and propose effective defensive strategies. The resulting taxonomy provides a structured foundation for designing and evaluating secure blockchain interoperability solutions.