Advanced vibration control technologies are in high demand for equipment such as aircraft and ships. Currently, most systems separate vibration absorption and isolation design, and existing isolation designs cannot effectively enhance the isolation of low-frequency line spectra. There is an urgent need to develop integrated vibration absorption and isolation designs and enhance low-frequency line spectrum control. In response to this need, this paper focuses on a typical Euler beam and investigates the propagation characteristics of vibrations in both transverse and longitudinal directions, the principles of integrated vibration absorption and isolation design, and the synergistic regulation of bandgaps, based on acoustic metamaterial bandgap wave-insulating vibration control configurations and analytical methods. Ultimately, without adding additional structures, the use of wave-insulating vibration control devices generates multiple modes of vibration absorption and isolation simultaneously, achieving an integrated low-frequency, broadband, and high-efficiency vibration absorption and isolation design. In the transverse vibration isolation pathway, this method achieves broadband vibration isolation while introducing localized resonant bandgaps that significantly enhance low-frequency vibration isolation. In the longitudinal (forward propagation) pathway, in addition to near-zero and Bragg bandgaps, multilayer isolators generate multimodal local resonant bandgaps, achieving low-frequency broadband vibration absorption and effective control across the entire frequency range. This paper elucidates the synergistic modulation of longitudinal and transverse bandgaps, showing that by superimposing these bandgaps, an impressive bandgap ratio of 87.3% below 100 Hz across the entire frequency range can be achieved. Furthermore, an entity structure was designed, and the accuracy of the analytical results was verified using the finite element method. The findings provide feasible design ideas for the integrated vibration absorption and isolation of complex structures such as beams, plates, pipelines, and frames.