  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.
