The exponential growth in global mobile data traffic, especially with regards to the massive deployment of devices envisioned for the fifth generation (5G) mobile networks, has given impetus to exploring new spectrum opportunities to support the new traffic demands. The millimeter wave (mmWave) frequency band is considered as a potential candidate for alleviating the spectrum scarcity. Moreover, the concept of multi-tier networks has gained popularity, especially for dense network environments. In this article, we deviate from the conventional multi-tier networks and employ the concept of control-data separation architecture (CDSA), which comprises of a control base station (CBS) overlaying the data base station (DBS). We assume that the CBS operates on the sub-6 GHz single band, while the DBS possesses a dual-band mmWave capability, i.e., 26 GHz unlicensed band and 60 GHz licensed band. We formulate a multi-objective optimization (MOO) problem, which jointly optimizes conflicting objectives: the spectral efficiency (SE) and the energy efficiency (EE). The unique aspect of this work includes the analysis of a joint radio resource allocation algorithm based on Lagrangian Dual Decomposition (LDD) and we compare the proposed algorithm with the maximal-rate (maxRx), dynamic sub-carrier allocation (DSA) and joint power and rate adaptation (JPRA) algorithms to show the performance gains achieved by the proposed algorithm.