This game is a combination of Monochromatic Chess (where pieces are not allowed to change color) with V.R. Parton's Alice Chess (where pieces change board each time they move), with the array from George Deckle Sr.'s Lilliputian Chess. It is played on a stack of two 6x7 boards.
 
A piece always ends up on a square of the same color on which it started. When it makes a move -- either capturing or non-capturing -- to a square of the other color, after the move completes, the piece `falls` through to the other board, where the checking is reversed, thus keeping on the same color. If the square on the other board is occupied, then the move is not allowed.
 
The King may not move into an attacked square, then fall out of it. However, check may be blocked by a piece falling through.
 
Pawns promote at the back row of either board.
 
A longer, more detailed description of Lilliputian Monochromatic Alice Chess can be found at http://www.chessvariants.com/large.dir/contest84/lma-chess.html.