We present a simple unified model that accounts for properties of X-ray emission from the three middle-aged pulsars PSR 1055-52, PSR 0656+14, and PSR 0630+18 (Geminga). The X-ray radiation from these objects is pulsed more strongly at energies above a transition point around 0.5 keV. In addition, the phase of the pulses shifts by about 80°-100° around the same point. Geminga also has the peculiarity that its pulsed fraction decreases in the 0.3-0.5 keV energy range, attaining a minimum near 0.5 keV. We show that a two-component hydrogen atmosphere is able to account for these disparate features. In our model, the hotter component is powered by particle bombardment and is restricted to the polar regions, while the cooler one covers the entire stellar surface. The two components also differ in their emission patterns, with the hard and soft contributions coming from areas radiating into fan and pencil beams, respectively.