Freely switching light transmission and absorption via an achromatic reflectionless screen is highly desired for many photonic applications (e.g., energy-harvesting, cloaking, etc.), but available meta-devices often exhibit reflections out of their narrow working bands. Here, we rigorously demonstrate that an optical metasurface formed by two resonator arrays coupled vertically can be perfectly reflectionless at all frequencies below the first diffraction mode, when the near-field (NF) and far-field (FF) couplings between two constitutional resonators satisfy certain conditions. Tuning intrinsic loss of the system can further modulate the ratio between light transmission and absorption, yet keeping reflection diminished strictly. Designing/fabricating a series of metasurfaces with different inter-resonator configurations, we experimentally illustrate how varying inter-resonator NF and FF couplings can drive the system to transit between different phase regions in a generic phase diagram. In particular, we experimentally demonstrate that a realistic metasurface satisfying the discovered criteria exhibits the desired achromatic reflectionless property within 160–220 THz (0–225 THz in simulation), yet behaving as a perfect absorber at ~ 203 THz. Our findings pave the road to realize meta-devices exhibiting designable transmission/absorption spectra immune from reflections, which may find many applications in practice.