  We analyze the structure and stability of the transition layer (or front)
that connects the cold neutral medium and warm neutral medium in the
plane-parallel geometry. Such fronts appear in recent numerical simulations of
a thermally bistable interstellar medium. The front becomes an evaporation or
condensation front depending on the surrounding pressure. The stability
analysis is performed in both long- and short-wavelength approximations. We
find that the plane-parallel evaporation front is unstable under corrugational
deformations, whereas the condensation front seems to be stable. The
instability is analogous to the Darrieus-Landau instability in combustion
front. The growth rate of the instability is proportional to the speed of the
evaporation flow and the corrugation wavenumber for modes with wavelength much
longer than the thickness of the front, and it is suppressed at scales
approximately equal to the thickness of the front. The timescale of the
instability is smaller than the cooling timescale of the warm neutral medium
($\sim 1$ Myr), and can be as small as the cooling timescale of the cold
neutral medium ($\sim 0.01-0.1$ Myr). Thus, this instability should be one of
the processes for driving the interstellar turbulence.
