Using pulsed gradient spin-echo NMR, we studied molecular self-diffusion in aligned samples of a hybrid lyotropic lamellar L(alpha) phase. This composite organic-inorganic material was obtained by doping the lamellar phase of the nonionic surfactant Brij-30 with the [PW(12)O(40)](3-) polyoxometalate (POM). Both water and POM self-diffusion display a large anisotropy, as diffusion is severely restricted along the normal to the bilayers. Water diffusion in planes parallel to the bilayers does not depend on the POM concentration but depends on the lamellar period, which is due to a variable fraction of "bound" water molecules. POM diffusion in the hybrid L(alpha) phase is almost 2 orders of magnitude slower than in aqueous solution. Moreover, it is not at all affected by the thickness of the aqueous medium separating the bilayers. This proves that the POM nanoparticles do not freely diffuse in the interbilayer aqueous space but adsorb onto the PEG brushes that cover both sides of the surfactant bilayers.