Control data separation architecture (CDSA) is a more efficient architecture to overcome the overhead issue than the conventional cellular networks, especially for the huge bursty traffic like Internet of Things, and over-the-top (OTT) content service. In this paper, we study the optimization issue of network energy efficiency of the CDSA-based heterogeneous cloud radio access networks (H-CRAN) networks, which has heterogeneous fronthaul between control base station (CBS) and data base stations (DBSs). We first present a modified power consumption model for the CDSA-based H-CRAN, and then formulate the optimization problem with constraint of overall capacity of wireless fronthaul. Then we work out the resource assignment and power allocation by the convex relaxation approach using fractional programming, norm approximation, and Lagrangian dual decomposition method, with a derived the close-form optimal solution. Finally, we verify the proposed method by system- level simulation. The comprehensive simulation results show that our proposed algorithm has 10% EE gain compared to the static algorithm, and the CDSA-based H-CRAN networks can achieve up to 14% EE gain compared to the conventional network even under strict fronthaul capacity limit.