Harnessing multi-level electron transitions, Rydberg Atomic REceivers (RAREs) can detect wireless signals across a wide range of frequency bands, from Megahertz to Terahertz. This capability enables multi-band wireless communications and sensing (CommunSense). Existing research on multi-band RAREs primarily focuses on experimental demonstrations, lacking a tractable model to mathematically characterize their mechanisms. This issue leaves the multi-band RARE as a black box and poses challenges in its practical applications. To fill in this gap, this paper investigates the underlying mechanism of multiband RAREs and explores their optimal performance. For the first time, an analytical transfer function with a closed-form expression for multi-band RAREs is derived by solving the quantum response of Rydberg atoms. It shows that a multiband RARE simultaneously serves as a multi-band atomic mixer for down-converting multi-band signals and a multi-band atomic amplifier that reflects its sensitivity to each band. Further analysis of the atomic amplifier unveils that the intrinsic gain at each frequency band can be decoupled into a global gain term and a Rabi attention term. The former determines the overall sensitivity of a RARE to all frequency bands of wireless signals. The latter influences the allocation of the overall sensitivity to each frequency band, representing a unique attention mechanism of multi-band RAREs. The optimal design of the global gain is provided to maximize the overall sensitivity of multi-band RAREs. Subsequently, the optimal Rabi attentions are also derived to maximize the practical multi-band CommunSense performance. An experiment platform is built to validate the effectiveness of the derived transfer function, and numerical results confirm the superiority of multi-band RAREs.