The interplay between spin, valley and layer pseudospin in layered transition-metal dichalcogenides (TMDs) is of fundamental importance in designing multifunctional pseudospintronic devices. In our recent work, we have investigated the quantum transport of spin, valley and layer degrees of freedoms (DOFs) through a magnetoelectric barrier in AB-stacked bilayer TMDs. In this talk, after a short exposition of some preliminaries on the subject, we present some of our main results. The talk would be accessible to the public audience (in physics).