Electric-field transients covering the extremely wide frequency range from 0.5 to 26 THz are generated in the organic nonlinear crystal 4-N,N-dimethylamino-4'-N'-methylstilbazolium 2,4,6-trimethylbenzenesulfonate (DSTMS). Parametric difference frequency mixing within the spectrum of 25-fs amplified pulses centered at 800 nm provides a highly stable broadband output with an electric-field amplitude of up to several hundred kilovolts/cm. The high stability of the terahertz pulse parameters allows for sensitive phase-resolved broadband spectroscopy of optically thick crystalline samples.