This study extends Combinatorial Homomorphic Automatic Differentiation (CHAD) to programs that include partial functions, data-dependent conditionals, and iterative statements (while loops). While maintaining the structure-preserving semantics principle of the original CHAD, we introduce 'iteration-extensive indexed categories' as a theoretical basis for iterative statements. Through this, we extend the CHAD transformation with the only structure-preserving function (iterative Freyd category morphism) that maps the iterative framework of the source language to the container categories of the target language, and prove the correctness of the extended transformation using a categorical model. The key is to structurally preserve the iterative structure of the source language through the mapping to the container categories of the target language.