A compact, solid-state accelerating structure based on surface waves is proposed and experimentally characterized. The structure, consisting of two SiC layers epitaxially grown on Si slabs and separated from each other by a subwavelength acceleration channel, is shown to support both longitudinal (accelerating) and transverse (deflecting) surface modes. Both modes are experimentally excited and characterized by performing angle-resolved spectroscopy with a wavelength-tunable carbon dioxide laser. Phase velocities of superluminous and subluminous modes are experimentally demonstrated, paving the way for tabletop charged particle acceleration. The same structure can be used for optical characterization of ultrashort electron bunches that generate longitudinal and transverse Cherenkov radiation.