We study, by a quasi-elastic-light-scattering technique, the hydrodynamics of a composite system, called a ferrosmectic phase, in which small magnetic particles are incorporated in a lyotropic smectic medium. Layer displacement fluctuations and Brownian diffusion of the particles are coupled in general. We study here the particle motion, varying both the orientation of the scattering wave vector and its magnitude. There is a strong anisotropy of the particle diffusion coefficient tensor: the motion parallel to the layers is only slightly slowed down with respect to an isotropic medium, while there is no detectable permeation of the particles through the layers; these results are compared to a model of confinement between two walls.