Crosstalk in optical switch is an intrinsic drawback of optical networks, and avoiding crosstalk is important for making optical network work properly. Horizontal expansion and vertical stacking are two basic techniques for creating nonblocking multistage interconnection networks (MINs). Rearrangeable (nonblocking) optical MINs are feasible since they have lower complexity than their strictly nonblocking counterparts. In this paper, we study the crosstalk-free permutations in rearrangeable optical MINs built on a combination of horizontal expansion and vertical stacking of banyan networks, and provide a scheme for realizing crosstalk-free permutations in this kind of optical MINs. The basic idea of this scheme is to first decompose a permutation into multiple partial permutations by using Euler Split technique, then route and realize each of these partial permutations crosstalk-free in one plane (stacked copy) of a MIN based on both the Euler Split technique and self-routing property of a banyan network. The tradeoff between the overall time complexity and hardware cost of this class of MINs is also explored in this paper.