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Feature Engineering (FE) is pivotal in automated machine learning (AutoML) but remains a bottleneck for traditional methods, which treat it as a black-box search, operating within rigid, predefined search spaces and lacking domain awareness. While Large Language Models (LLMs) offer a promising alternative by leveraging semantic reasoning to generate unbounded operators, existing methods fail to construct free-form FE pipelines, remaining confined to isolated subtasks such as feature generation. Most importantly, they are rarely optimized jointly with hyperparameter optimization (HPO) of the ML model, leading to greedy "FE-then-HPO" workflows that cannot capture strong FE-HPO interactions. In this paper, we present CoFEH, a collaborative framework that interleaves LLM-based FE and Bayesian HPO for robust end-to-end AutoML. CoFEH uses an LLM-driven FE optimizer powered by Tree of Thought (ToT) to explore flexible FE pipelines, a Bayesian optimization (BO) module to solve HPO, and a dynamic optimizer selector that realizes interleaved optimization by adaptively scheduling FE and HPO steps. Crucially, we introduce a mutual conditioning mechanism that shares context between LLM and BO, enabling mutually informed decisions. Experiments show that CoFEH not only outperforms traditional and LLM-based FE baselines, but also achieves superior end-to-end performance under joint optimization.