To suppress combustion instabilities, Helmholtz resonators are typically used as acoustic dampers to dissipate acoustic waves. However, they tend to be effective over a narrow-frequency bandwidth. Furthermore, the space available for applying such resonators is limited. To effectively use the space and to reduce the transmission of acoustic waves, a parallel-coupled Helmholtz resonator network, with two resonators connected via a thin compliant membrane, was designed and experimentally tested. It was found that the compliant membrane motion gave rise to the production of additional transmission loss peaks at nonresonant frequencies of the resonators. A numerical model was then developed to simulate the experiments. Green’s function approach was used to determine the membrane motion, which was associated with the rate of resonators cavities volume change. Good agreement between the numerical and experimental results was observed. To damp frequency-varying noise, the membrane vibration was actively tuned by implementing a trust-region Newton conjugate-gradient method. Transmission loss was found to increase to approximately 25 dB over a broad frequency range. Finally, experimental tests of other resonator network configurations were conducted, which included blocking one of the resonator necks or removing the diaphragm.