This paper focuses on the construction of multidimensional biorthogonal multiwavelets and the perfect reconstruction multifilter banks. Based on the Hermite-Neville filter, two lifting structures have been proposed and systematically investigated, and a general design framework has been developed for building biorthogonal multiwavelets and Hermite interpolation filter banks with any multiplicity for any lattice in any dimension with any number of primal and dual vanishing moments. The construction is an important generalization of the Neville-based lifting scheme and inherits all of the advantages of lifting schemes such as fast transform, in-place computation and integer-to-integer transforms. Our multiwavelet systems preserve most of the desirable properties for applications, such as interpolating, short support, symmetry, and high vanishing moments.