Waves in patchy-saturated rocks are attenuated through the mechanism of wave-induced pressure diffusion. Previous studies reveal that attenuation and phase-velocity dispersion depend on the fluid patch size and distribution. These patch characteristics in turn can be influenced by capillary forces. The effect of capillarity on wave attenuation in patchy-saturated rocks is not fully understood. We studied the combined effects of wave-induced pressure diffusion and capillarity on acoustic signatures. To do so we made use of the concept of patch membrane stiffness as a macroscopic expression of capillarity. We incorporated the membrane stiffness into the continuous random media model of patchy saturation. The membrane stiffness is associated with a pressure discontinuity at patch interfaces. This pressure discontinuity impedes wave-induced pressure diffusion and, therefore, reduces wave attenuation. Conversely, the phase velocity increases due to additional capillarity reinforcement. We applied this capillarity-extended random media model to interpret velocity-saturation relations (VSR) and attenuation-saturation relations (ASR) retrieved from an ultrasonically monitored core flooding experiment. Because the fluid distribution is approximately known from accompanying computerized tomographic images, all but one required model input parameters can be inferred. The elusive input parameter is a shape factor quantifying the geometric irregularity of the pore channels. We found, however, that the experimental data can be consistently modeled only if the capillarity effect is accounted for. The results suggested that wave-induced fluid-pressure diffusion at mesoscopic patches in conjunction with capillary action can have important implications for interpreting ultrasonic VSR and ASR in patchy-saturated rocks.