Session typesÐa family of type systems for message-passing concurrencyÐhave been subject to many extensions, where each extension comes with a separate proof of type safety. These extensions cannot be readily combined, and their proofs of type safety are generally not machine checked, making their correctness less trustworthy. We overcome these shortcomings with a semantic approach to binary asynchronous affine session types, by developing a logical relations model in Coq using the Iris program logic. We demonstrate the power of our approach by combining various forms of polymorphism and recursion, asynchronous subtyping, references, and locks/mutexes. As an additional benefit of the semantic approach, we demonstrate how to manually prove typing judgements of racy, but safe, programs that cannot be type checked using only the rules of the type system.