Full-wave electromagnetic interaction of two regular arrays of dipole scatterers is considered. To calculate the local field acting on a particle in the arrays a method analogous to the Lorenz-Lorentz approach is used. The contributions from distant and near scatterers are separately evaluated. The contribution from the near particles is determined by the direct summation of the dipole fields. Distant particles are replaced by a continuous distribution of dipole moments. The full-wave formulas representing the fields created by a continuous distribution sheet with a circular hole of a certain radius are obtained for the case when the observation point is located on the hole axis at an arbitrary distance from the hole center. Numerical examples illustrating the physical aspects of the obtained results are given. As application examples, the reflection from double arrays of magnetically polarizable particles are considered. This is relevant to the design of radar absorbing coverings based on thin layers of artificial magnetics. An explicit analytical solution for the reflection coefficient is given.