  We study a diffusion approximation for a model of stochastic motion of a
particle in one spatial dimension. The velocity of the particle is constant but
the direction of the motion undergoes random changes with a Poisson clock.
Moreover, the particle interacts with an interface in such a way that it can
randomly be reflected, transmitted, or killed, and the corresponding
probabilities depend on whether the particle arrives at the interface from the
left, or right. We prove that the limit process is a minimal Brownian motion,
if the probability of killing is positive. In the case of no killing, the limit
is a skew Brownian motion.
