The Anderson delocalization-localization transition is studied in multilayered systems with randomly placed interlayer bonds of density $p$ and strength $t$. In the absence of diagonal disorder (W=0), following an appropriate perturbation expansion, we estimate the mean free paths in the main directions and verify by scaling of the conductance that the states remain extended for any finite $p$, despite the interlayer disorder. In the presence of additional diagonal disorder ($W > 0$) we obtain an Anderson transition with critical disorder $W_c$ and localization length exponent $ u$ independently of the direction. The critical conductance distribution $P_{c}(g)$ varies, however, for the parallel and the perpendicular directions. The results are discussed in connection to disordered anisotropic materials.
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