I'm trying to implement mouse interaction in a 2D isometric game, but I'm not sure if it's possible given the coordinate system used for tile maps in the game.

I've read some helpful things like this. However, this game's coordinate system is "jagged" (for lack of a better word), and looks like this:

Is it even possible to map mouse coordinates to this successfully, since the y-axis can't be drawn on this tile-map as a straight line?

I've thought about doing odd-y-value translations and even-y-value translations with two different matrices, but that only makes sense going from tile to screen.