You can do this with two layers, which I'll refer to as "Foreground" and "Background".
The Foreground layer is arranged above the Background layer, as you'd probably guess.
On the Foreground layer, place the CharTiles and ColorTiles.
If we just stop here, the problem is that the Background layer will be tinted by the ColorTiles too, even though the ColorTiles are on a different layer. fortunately there's a solution.
In the layer panel, select the Foreground layer, and in the property panel, enable "Force own texture".
This will prevent the multiply blend of the ColorTiles from affecting any other layer, and so the ColorTiles will only colorize the CharTiles.
For this to work, the char tiles will need to be white text on a transparent background. The ColorTiles will have no effect where they overlap transparency.
Now you can put whatever you want in on the Background layer and it will show up behind your colorized ANSI characters.
Since your CharTiles will be under your ColorTiles, you may need to temporarily switch their Z-orders to edit one or the other.More on "Force own texture"
This setting will force the layer to render it's contents starting from a transparent background, instead of starting from the rendered result of all the layers below it. When a "Force own texture" layer has rendered all it's contents, it will then be pasted on top of the rendered result of all the layers below it. This is why blend effects for objects on a "Force own texture" layer will be isolated from other layers.Using Black on transparent text
If you'd rather work with black text on a transparent background, you can replace the ColorTiles' "Multiply" blend effect to a "Screen" blend effect.
"Screen" blend is identical to "Multiply" blend except flipped upside down in the 0 to 1 color value space. Screen inverts the inputs, multiplies them, and inverts the result.
i.e. screen( a , b ) = 1 - mult( 1 - a , 1 - b )
If you screen any image with white(1,1,1,) you'll always get white. Screen an image with black(0,0,0) and you'll always get the original image unchanged. Screen with middle-gray(0.5, 0.5, 0.5), and you'll get all the image's brightness values moved 50% closer to white. Light-gray(0.9, 0.9, 0.9) will move the image's brightness values 90% closer to white.