Dual-band shared-aperture Fabry-Pérot cavity (DS-FPC) antennas with single-layer partially reflective surface (PRS) are inherently limited in the achievable frequency ratio. This paper analyzes such antennas to derive the feasible range of frequency ratio and thereafter proposes a dual-band shared-aperture antenna that can fill the frequency ratio gap. The proposed antenna integrates a short backfire antenna (SBA) for the low band (LB) and a Fabry-Pérot cavity (FPC) antenna for the high band (HB), utilizing a shared single-layer PRS and a parasitic element. In LB, using a parasitic element that is transparent for HB, the SBA works well despite its low profile. In HB, the FPC antenna works with the first-order FPC mode. A prototype working at 5.5GHz and 9GHz was fabricated and measured. The overall height of the antenna is 0.36 and 0.59 wavelength in LB and HB, respectively. The prototype achieves 7.3% and 6.7% of measured overlapping 10dB impedance bandwidth and 3dB realized gain bandwidth, as well as peak realized gains of 10.3 and 14.6dBi, in LB and HB, respectively.