Reconciling dependent product and classical logic with call-by-value evaluation is a difficult problem. It is the first step toward a classical proof system for an ML-like language. In such a system, the introduction rule for universal quantification and the elimination rule for dependent product need to be restricted: they can only be applied to values. This value restriction is acceptable for universal quantification (ML-like polymorphism) but makes dependent product unusable in practice. In order to circumvent this limitation we introduce new typing rules and prove their consistency by constructing a realizability model in three layers (values, stacks and terms). Such a technique has already been used to account for classical ML-like polymorphism in call-by-value, and we here extend it to handle dependent product. The main idea is to internalize observational equivalence as a new non-computable operation in the calculus. A crucial property of the obtained model is that the biorthogonal of a set of values which is closed under observational equivalence does not contain more values than the original set.