  We present a pulsar-atmosphere (PA) model for modulated thermal X-ray
emission from cooling magnetized neutron stars. The model synthesizes the
spectral properties of detailed stellar atmosphere calculations with the
non-uniform surface properties anticipated for isolated, aging radio pulsars,
and general relativistic effects on photon trajectories. We analyze the
archival Chandra observations of the middle-aged radio pulsar PSR 0656+14 with
the PA model and find it is an excellent representation of the phase-averaged
X-ray spectrum for a broad range of polar effective temperature T_p and column
density N_H ~ 10^{20} cm^{-2}. The spectral fits favor a sub-solar neutron star
mass M < 1.0 M_{\sun}, a large radius R=15-16 km for a source distance d ~ 190
pc, while retaining consistency with theoretical neutron star
equations-of-state. The modulated spectrum constrains the angular displacement
of the pulsar spin axis to 30 +/- 2 \arcdeg with respect to the line of sight.
