The best I could come up with would be:
Assign some property denoting “hole” tiles to be recognized different from “floor” and “wall” tiles. Normally, while your character is not “jumping”, when they come in contact with the hole tile they fall down it and die, or just act as a solid tile (your preference).
When the player presses the jump key, set “jumping” to true and the character will “ignore” tiles tagged as holes, allowing them to move safely over it. The jump boolean would return to false after the player has traveled a certain number of tiles (2 is probably what you’re looking for). The jump command should require you set a direction to jump (like LEFT ARROW + JUMP), and not allow the player to change directions again until they have landed. To simplify how long the jump should last, you may even replace the boolean Jump variable with a float Jump variable that is set to a number on jump and then decrements at a fixed rate until it reaches 0 again. (then you could have a property bool IsJumping { get { return Jump > 0; } } to check if the player is in midair). The Jump variable as a float would also give you a means of judging which frame of jumping animation to display.