Social engineering malware, which exploits both technical and human vulnerabilities, presents challenging for individuals and organizations. However, existing studies typically focus on either technical or human vulnerabilities through case studies or questionnaires, ignoring their combined importance in mitigating such threats. This study pioneers the introduction of a mathematical model to analyze and mitigate the dynamics associated with these combined vulnerabilities. To achieve this, this study proposes an innovative framework, which integrates (a) acoupled malware-opinion dynamics modelto capture the interplay between both types of vulnerabilities, and (b) anoptimal impulse control approachto strategically mitigatingsocial engineering malware. Within this framework, we define an optimization problem, aimed at balancing control costs and malware severity. We derive theoretical conditions for optimal impulse strategies that achieve this balance and develop an iterative algorithm, the convergence and scalability of which have been empirically validated. Experimental results on three real-world social networks and synthetic scale-free networks demonstrate that our strategies consistently achieve an optimal balance by minimizing total expenses, including control costs and losses associated with malware. This finding underscores the effectiveness of routine patching and ongoing security awareness training in standard cybersecurity practices. Further experiments indicate that the strategic, early, and frequent deployment of patches in specific scenarios can effectively reduce unnecessary losses, enhancing overall cybersecurity resilience.