At both Chess and Alice Chess, the Bishops are restricted to one half of
the squares. But at Alice Chess, this holds true also for the Knights, and
for the Pawns once they've completed their first move.

So you can paint the squares in eight different colors, each color
meaning:
This square will not accept:
1) the dark-square Bishops (OR the light-square Bishops)
2) the Knights which started on a dark square (OR the Knights which
started on a light square)
3) the white Pawns whose first advance was of two squares and the black
Pawns whose first advance was of one square (OR the white Pawns whose
first advance was of one square and the black Pawns whose first advance
was of two squares)

This amounts to eight different square types.
Something like:

   1 2 1 2 1 2 1 2    3 4 3 4 3 4 3 4
   5 6 5 6 5 6 5 6    7 8 7 8 7 8 7 8
   1 2 1 2 1 2 1 2    3 4 3 4 3 4 3 4
   5 6 5 6 5 6 5 6    7 8 7 8 7 8 7 8
   1 2 1 2 1 2 1 2    3 4 3 4 3 4 3 4
   5 6 5 6 5 6 5 6    7 8 7 8 7 8 7 8
   1 2 1 2 1 2 1 2    3 4 3 4 3 4 3 4
   5 6 5 6 5 6 5 6    7 8 7 8 7 8 7 8

Or you can have three ways of painting the squares:
light and dark as usual, in two colors I'm referring to as B-colors, to
separate the Bishops in two classes (1368 vs 2457)
reversing the colors of one chessboard, in two N-colors, to separate the
Knights in two classes (1467 vs 2358)
even-numbered rows of one chessboard and odd-numbered rows of the other
chessboard, and vice versa, in two P-colors, to separate the Pawns in two
classes (1278 vs 3456)
However, a Bishop can be captured only by a Bishop of the same B-color,
while a Knight can be captured only by a Knight of the other N-color and a
Pawn only by a Pawn of the other P-color.