A new approach for coupling lattice and whole core neutron transport calculations, which was previously applied to two-dimensional problems, is generalized to three-dimensions. The method eliminates the need for spatial homogenization of cross sections at the pin-cell or fuel assembly level. This is accomplished by expressing the interface conditions for heterogeneous pin-cell sized response matrices as spherical harmonic expansions. The expansions are partitioned into low and high order moments, and reflective conditions applied to the high order moments. This results in response matrices of greatly decreased dimension that partially decouple periodic lattice effects from global flux gradients. The method is implemented as modifications to the three-dimensional variational nodal code VARIANT, and applied to a MOX fuel assembly with partially inserted control rods as specified in the OECD/NEA C5G7 benchmark.