We calculate the transmission spectra of a flux qubit coupled to a dissipative resonator in the ultrastrong coupling regime. Such a qubit-oscillator system constitutes the building block of superconducting circuit QED platforms. The calculated transmission of a weak probe field quantifies the response of the qubit, in frequency domain, under the sole influence of the oscillator and of its dissipative environment, an Ohmic heat bath. We find the distinctive features of the qubit-resonator system, namely two-dip structures in the calculated transmission, modified by the presence of the dissipative environment. The relative magnitude, positions, and broadening of the dips are determined by the interplay among qubit-oscillator detuning, the strength of their coupling, and the interaction with the heat bath. I. INTRODUCTION Current developments in circuit quantum electrodynamics (QED) are establishing superconducting devices as leading platforms for quantum information and simulations [1-5]. In particular, quantum optics experiments with qubit coupled to superconducting resonators are now performed in (and beyond) the so-called ultrastrong coupling (USC) regime, with the qubitresonator coupling reaching the same order of magnitude of the qubit splitting and resonator frequency [6-12]. The qubits are essentially based on superconducting circuits interrupted by Josephson junctions, the nonlinear elements that provide the anharmonicity required to singleout the two lowest energy states [13]. In the flux configuration, the qubit states are superpositions of the eigenstates of the magnetic flux operator associated to clockwise and anti-clockwise circulating supercurrents, corresponding to the two lowest energy eigenstates of a double-well potential seen by the flux coordinate. The double-well can be biased by applying an external magnetic flux and transitions between states in this qubit basis, where the states are localized arXiv:1906.05808v3 [quant-ph]