Future mobile networks are supposed to serve high data rates required by users. To accommodate the high data rates, a direct communication between nearby mobile terminals (MTs), known as Device-to-device (D2D) communication, can be exploited. Furthermore, a communication in high frequency bands, such as, visible light communication (VLC), is also foreseen as an enabler for the high data rates. In conventional D2D communication, pairs of the MTs should reuse the same frequencies to keep a high spectral efficiency of the system. However, this implies either interference among the D2D pairs or utilization of complex and advanced resource allocation algorithms. In this paper, we propose a new concept for D2D communication combining VLC and RF technologies in order to maximize capacity of the system. This paper provides an analysis of the operational limits for the proposed concept and investigates capacity gains introduced by the combined usage of RF and VLC bands for D2D. Moreover, we discuss several practical issues related to the proposed RF-VLC D2D concept. Performed analyses show that the RF-VLC D2D is able to improve the capacity in an indoor scenario by a factor of 4.1 and 1.5 when compared to stand-alone RF D2D and VLC D2D, respectively.