The maximal number of knights of a single color that can be placed on a chessboard without any knight being one knights-move away from any other is 32; such a position may easily be achieved by placing all 32 knights on squares of the same color.
If one uses both black pieces and white pieces, it's possible to place 24 knights of each color (48 total) on the board without any knight being attacked by a knight of the opposite color. One simple approach is to place 24 white knights on the first three ranks, and 24 black knights on the last three. That position is but one of many, which can accommodate 24 knights of each color.
Is it possible to either place 24 knights of one color and more than 24 of the other or prove the impossibility of doing so? Note that if one may arbitrarily choose the number of knights of each color, one could easily place 62 knights (61 white and one black) or, for that matter, 64 (all white). To be of interest, I think it is possible to rank solutions by the number of pieces in the "shorter" army and then by the number of pieces in the other.