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The Atacama Large Millimeter/sub-millimeter Array (ALMA) has provided us with an excellent diagnostic tool for studies of the dynamics of the Solar chromosphere, albeit through a single receiver band at one time presently. Each ALMA band consists of four sub-bands that are comprised of several spectral channels. To date, however, the spectral domain has been neglected in favour of ensuring optimal imaging, so that time-series observations have been mostly limited to full-band data products, thereby limiting studies to a single chromospheric layer. Here, we report the first observations of a dynamical event (i.e. wave propagation) for which the ALMA Band 3 data (centred at 3\,mm; 100\,GHz) is split into a lower and an upper sideband. In principle, this approach is aimed at mapping slightly different layers in the Solar atmosphere. The side-band data were reduced together with the Solar ALMA Pipeline (SoAP), resulting in time series of brightness-temperature maps for each side-band. Through a phase analysis of a magnetically quiet region, where purely acoustic waves are expected to dominate, the average height difference between the two side-bands is estimated as $73\pm16$~km. Furthermore, we examined the propagation of transverse waves in small-scale bright structures by means of wavelet phase analysis between oscillations at the two atmospheric heights. We find 6\% of the waves to be standing, while 54\% and 46\% of the remaining waves are propagating upwards and downwards, respectively, with absolute propagating speeds on the order of $\approx96$~km/s, resulting in a mean energy flux of $3800$\,W/m$^2$.