Integration of the promising Millimeter wave (mmWave) technology into the existing cellular network is one of the main challenges towards a unified multi-Gbps 5G cellular network. However, due to its short transmission range accompanied with the inevitable use of highly directional communication, directly controlling the access of mmWave small cells (SCs) using the legacy LTE eNB using conventional LTE/WLANs interworking techniques seems to be an inefficient solution. In this paper, a novel radio access network (RAN)-level hierarchical multi-band heterogeneous network (HetNet) architecture is proposed to efficiently overlay mmWave SCs over the legacy LTE eNB. In this architecture, the Wi-Fi medium coverage band is used as an intermediate level between the large coverage LTE band and the small coverage mmWave band. The Wi-Fi band via the proposed concept of Wi-Fi/mmWave sub-clouds enables precise control to the access over the mmWave band; while, the LTE eNB only controls the access over the distributed Wi-Fi/mmWave sub-clouds. Accordingly, a novel concept of two-level control and user data planes splitting, 2C/U, is introduced in this paper. In this 2C/U plane splitting, the LTE eNB controls the network access over the distributed sub-clouds using C1-plane, while, the C2-plane, provided by the Wi-Fi band, controls the access over the distributed mmWave SCs inside the sub-clouds. Thanks to this distributed control, the mmWave band can be efficiently utilized and the complexity of the mmWave initial access can be highly reduced. Moreover, the associated signaling/processing load on both LTE eNB and core network (CN) can be highly relaxed. Analytical and numerical analysis assure the performance superiority of the proposed LTE/Wi-Fi/mmWave HetNet over the conventional LTE/mmWave HetNet