A frequency selective rasorber (FSR) with three transmission bands and three absorption bands is proposed in this paper. The FSR is constructed via cascading a lossy resistive surface and a multiple bandstop frequency selective surface (FSS) separated by air spacer. The transmission characteristics are obtained by the impedance poles of the interdigital capacitor-meander inductor resonators in the resistive surface and also the rectangular loop resonators in the FSS. The absorption bands are achieved using the ohmic loss of the resistors in the resistive surface along with the reflections of the FSS. The physical principle of operation of the multiband FSR is explained based on an equivalent circuit model. A prototype is fabricated and measured. The experimental results exhibit three transmission bands at 6.1 GHz, 8 GHz and 10 GHz with insertion loss below 0.9 dB, 0.8 dB and 0.8 dB, respectively. The effective absorption bands are in range of 7.05 GHz-7.55 GHz, 8.87-9.35 GHz and 12.59 GHz-14.22 GHz, respectively. The simulation results show the angular stability of the FSR response. In addition, the effect of FSR dimensions on the transmission/absorption bands is studied. INDEX TERMS Frequency selective rasorber, triple-band transmission, triple-band absorption, interdigitalcapacitor/meander-inductor resonator.