Understanding the cooperative action of metal and acid sites of bifunctional catalysts is essential for developing more efficient catalysts for greener chemical processes. We used in situ ATR-IR spectroscopy in tandem with modulation excitation spectroscopy (MES) and phase-sensitive detection (PSD) to examine the functioning of Pd/silica–alumina (Pd/SA) catalysts with different acidity of the support in the liquid-phase hydrogenation of acetophenone (AP). The spectroscopic studies revealed that AP was adsorbed on the Pd surface in η 1 (O) configuration and initially hydrogenated to 1-phenylethanol (PE) on the metallic Pd sites. On the Pd surface, PE was less strongly adsorbed than AP. PE was preferentially adsorbed on the acidic silica–alumina support via the C–OH group and subsequently dehydrated to styrene on the acidic sites. Hydrogen originating from dissociative adsorption on Pd sites is proposed to hydrogenate part of the formed styrene to ethylbenzene (EB). The intermediate styrene had a short lifetime under hydrogenation conditions. Increasing the support acidity by raising the atomic fraction of aluminum (Al × 100%/(Al + Si)) in SA from 0 to 70% promoted the styrene production, which in turn strongly enhanced the EB yield from 17.3% on Pd/silica to 54.3% on Pd/SA-70, respectively.