In recent years, many intriguing electromagnetic (EM) phenomena have come into being utilizing metasurfaces (MSs). However, most of them operate in either transmission or reflection mode, leaving the other half of the EM space completely unmodulated. Here, a kind of transmission-reflection-integrated multifunctional passive MS is proposed for entire-space electromagnetic wave manipulation, which can transmit the x-polarized EM wave and reflect the y-polarized EM wave from the upper and lower space, respectively. By introducing an H-shaped chiral grating-like micro-structure and open square patches into the unit, the MS acts not only as an efficient converter of linear-to-left-hand circular (LP-to-LHCP), linear-to-orthogonal (LP-to-XP), and linear-to-right-hand circular (LP-to-RHCP) polarization within the frequency bands of 3.05–3.25, 3.45–3.8, and 6.45–6.85 GHz, respectively, under the x-polarized EM wave, but also as an artificial magnetic conductor (AMC) within the frequency band of 12.6–13.5 GHz under the y-polarized EM wave. Additionally, the LP-to-XP polarization conversion ratio (PCR) is up to −0.52 dB at 3.8 GHz. To discuss the multiple functions of the elements to manipulate EM waves, the MS operating in transmission and reflection modes is designed and simulated. Furthermore, the proposed multifunctional passive MS is fabricated and experimentally measured. Both measured and simulated results confirm the prominent properties of the proposed MS, which validates the design’s viability. This design offers an efficient way to achieve multifunctional meta-devices, which may have latent applications in modern integrated systems.