Neural code models have demonstrated their efficacy across a range of code comprehension tasks, including vulnerability detection, code classification, automatic code summarization, completion, clone detection, etc. Yet, a substantial gap exists in our understanding of the robustness of models in the realm of code comprehension and its associated applications. To probe and illuminate the robustness of code, recent efforts have sought to employ NLP-like techniques to craft adversarial code instances, primarily by perturbing variable and token names. It's worth noting that the semantics of source code predominantly surface through its structural elements, such as abstract syntax trees and control flow graphs, which fundamentally differ from natural languages. The question remains open: Can we perturb the structural aspects of code while preserving its semantics, thereby generating more disruptive adversarial examples that elude current structural-unaware approaches? Moreover, orchestrating adaptive adversarial attacks on diverse neural code models with varying architectures poses formidable challenges, especially in real-world scenarios characterized by constraints on target model access and querying. In this paper, we introduce ALANCA, an active-learning guided adversarial attack framework tailored for neural code models. Leveraging semantic-preserving translations, combined with an adaptive adversarial discriminator and token selector, ALANCA excels in executing adversarial attacks with high success rates, exceptional generation quality, and adaptability across different target models. We substantiate ALANCA's efficacy through comprehensive evaluations across four distinct code comprehension tasks, demonstrating its ability to effectively confound a range of neural models, including pre-trained models and LLMs used in software engineering.