We explore the integrated structure (or the unity) of consciousness by examining the "phenomenological axioms" of the "integrated information theory of consciousness (IIT)" from the perspective of Husserlian phenomenology. After clarifying the notion of phenomenological axioms by drawing on resources from Edmund Husserl and Maurice Merleau-Ponty (Section 1), we develop a critique of the integration axiom by drawing on phenomenological analyses developed by Aron Gurwitsch and Merleau-Ponty (Section 2 & 3). This axiom is ambiguous. It can be read either atomistically as claiming that the phenomenal content of conscious experience is an integrated complex and holistically as claiming that it is an integrated Gestalt. We argue that the latter reading provides a better characterization of the internal structure of the phenomenal content. Furthermore, the integrated structure of consciousness is not confined to the phenomenal content, but it also extends into the subjective attitude (Section 4). Subjective attitudes and phenomenal contents are interdependent constituents that jointly make up conscious experiences. This implies a novel theoretical challenge to the scientific component of IIT, which is to explain how to accommodate the subjective dimension of consciousness into its explanatory scope (Section 5). IIT can respond in a few different ways, but most importantly, it cannot just ignore it once and for all. As one possible way to address the challenge, we propose introducing a novel construct, noetic complex, to develop a fine-grained model of the neural underpinning of consciousness (Section 6).