An integral equation (IE) approach in the spatial domain is developed to analyze the electromagnetic (EM) scattering from the multilayered doubly periodic array of three-dimensional (3-D) general objects. This approach applies the equivalence principle to the interior problem of each layer. Then, the tangential continuity condition is applied to build up the connection between layers. The application of the equivalence principle and connection scheme (EPACS) allows us to avoid of the use of multilayered double periodic Green's functions. For 2N identical layers, the elimination of the unknowns between top and bottom surfaces can be accelerated using the logarithm algorithm. In addition, this approach is extended to handle the semi-infinitely layered array in which a unit consisting of several layers is repeated infinitely in one direction. The main contribution of this paper is to extend previous work on the EPACS to handle the 3-D perfect electric conductor or dielectric objects with arbitrary shapes. Numerical results are provided to validate the present approach.