We demonstrate the existence of a novel quasiparticle: an exciton in a semiconductor doubly dressed with two photons of different wavelengths: near infrared cavity photon and terahertz (THz) photon, with the THz coupling strength approaching the ultra-strong coupling regime. This quasiparticle is composed of three different bosons, being a mixture of a matter-light quasiparticle. Our observations are confirmed by a detailed theoretical analysis, treating quantum mechanically all three bosonic fields. The doubly dressed quasiparticles retain the bosonic nature of their constituents, but their internal quantum structure strongly depends on the intensity of the applied terahertz field.The research on light -matter interaction in the strong coupling regime, when quantum light emitter and photons can coherently exchange energy, before the coherence is lost, is one of the fundamental problems in cavity quantum electrodynamics (QED). This problem was widely adopted in an atom -cavity system, described within renowned Jaynes-Cummings model and even beyond this limit, in the ultra-strong coupling regime. The system based on exciton-polaritons, quasiparticles composed from excitons in a semiconductor strongly coupled to the vacuum light field in the cavity, has many advantages. These quantum light emitters do not show fermion-like statistics, but are truly designed bosons that can exhibit non-equilibrium Bose-Einstein phase transition [1]. In the present manuscript, we study the phenomenon of double dressing: an exciton coupled to two photonic fields from distinct energy ranges: near-infrared (NIR) and terahertz (THz), which bares no direct analogy in atomic physics.Excitons, or bound electron-hole pairs, can be created by the absorption of a near infrared (NIR) photon in a semiconductor. The strong coupling [2-4] of excitons and photons in a high-quality microcavity structure results in the formation of exciton-polaritons, due to vacuum field Rabi coupling, evidenced by the appearance of lower polariton (LP) and upper polariton (UP) resonances [5]. The strong coupling regime can be achieved when the coupling strength is larger than the decoherence and the correct description of the system is in terms of new quantum eigenstates, or dressed quasiparticles. In a quantum well (QW), which confines the exciton into a plane, the internal structure of the exciton resembles that of a two-dimensional hydrogen atom. The transitions between the internal states lie in the THz range of the electromagnetic spectrum. The possibility to induce such transitions with THz photons was shown in Refs. 6-8. Upon intense THz illumination, close to the 1s-2p excitonic transition, Autler-Townes splitting of excitonic states has been observed [1, 9].In this letter we demonstrate the simultaneous dressing of excitons with NIR and THz photons. We observe the appearance of a third dressed polariton mode, the middle polariton (MP), which is accompanied by an energy shift of the upper and lower polariton states. We describe our observations with a quant...