A material's acoustic properties depend critically upon porosity. Doping a soft material with gas-filled microballoons permits a controlled variation of the porosity through a scalable fabrication process while generating well-tailored spherical cavities that are impermeable to liquids. However, evidence is lacking of how the nanometer-scale polymeric shell contributes to the overall effective material properties in the regime where the wavelength is comparable to the sample thickness. Here, we measure ultrasound transmission through a microballoon-doped soft material as a function of microballoon and impurity concentration, sample thickness, and frequency. The measured longitudinal wave speeds are an order of magnitude larger than those in similar systems where no shell is present, while the transverse wave speed is found to linearly increase with microballoon concentration, also in contrast to systems with no shell. Furthermore, we find the results are independent of the soft material's elastic moduli as well as a lesser contribution of the microballoon shell on material attenuation. The results are validated with a multiple scattering model and suggest the shell contributes significantly to the material's bulk acoustic properties despite its thickness being 4 orders of magnitude smaller than the acoustic wavelength. Our results demonstrate how a nanometer-scale interface between a gas cavity and a soft polymer can be used in the submicrometer design of acoustic materials, and are important for observations of such phenomena as strong interference effects in soft matter.