We explore the coupling of the charge degree of freedom of electrons confined in a GaAs/AlGaAs double quantum dot (DQD) to a superconducting transmon qubit in the circuit QED architecture. In this work, we realize a proof of concept experiment in which the coupling between a transmon qubit and a DQD qubit is mediated by virtual microwave photon excitations in a tunable high impedance SQUID array resonator, which acts as a quantum bus enabling long range coupling between dissimilar qubits. Our device hosts a DQD capacitively coupled to a SQUID array resonator, which in turn is coupled to a single island transmon. The device is further equipped with a flux line for fast control of the transmon frequency, and with a 50 Ω CPW resonator capacitively coupled to the transmon for readout. Realizing a well controlled interface between semiconductor and superconductor-based quantum computing architectures will allow to take full advantage of those two solid states quantum systems for hybrid-quantum processors and will enable the use of both charge and flux degrees of freedom in the same device. The methods and techniques developed in this work are expected to be transferable to other material systems.