Caching and cloud control are new technologies that were suggested to improve the performance of future wireless networks. Fog radio access networks (F-RANs) have been recently proposed to further improve the throughput of future cellular networks by exploiting these two technologies. In this paper, we study the cloud offloading gains achieved by utilizing F-RANs that admit enhanced remote radio heads (eRRHs) with heterogeneous wireless technologies, namely, LTE and WiFi. This F-RAN architecture thus allows widely proliferating smart phone devices to receive two packets simultaneously from their in-built LTE and WiFi interfaces. We first formulate the general cloud base station (CBS) offloading problem as an optimization problem over a dual conflict graph, which is proven to be intractable. Thus, we formulate an online version of the CBS offloading problem in heterogeneous F-RANs as a weighted graph coloring problem and show it is NP-hard. We then devise a novel opportunistic network coding (ONC)-assisted heuristic solution to this problem, which divides it into two subproblems and solves each subproblem independently. We derive lower bounds on the online and aggregate CBS offloading performances of our proposed scheme and analyze its complexity. The simulations quantify the gains achieved by our proposed heterogeneous F-RAN solution compared with the traditional homogeneous F-RAN scheme and the derived lower bounds in terms of both CBS offloading and throughput.