Maybe not an answer

I think that Inset[] is not what you need.

Look what happens when you resize a graphic with some Inset[]  :

What you need is rather a layout that doesn't change when resizing.

Like this :

height = 125; cb = MatrixPlot[ Table[Mod[i + j, 2], {i, 1, 2}, {j, 1, 8}] , ColorFunction -> "BlueGreenYellow" , ImageSize -> {Automatic, 2*height} ]; p1 = MatrixPlot[ Table[1, {i, 1, 1}, {j, 1, 2}] , Mesh -> True , ColorFunction -> ColorData["DarkRainbow"] , ImageSize -> {Automatic, height} ]; Graphics[{cb[[1, {1, 2}]], Translate[p1[[1, {1, 2}]], {0, 2}]}, Frame -> True] 

Maybe not an answer

I think that Inset[] is not what you need.

This is what is happening when one resizes a graphic with some Inset[] without the fourth argument :

If you need a layout that doesn't change when resizing, you can use the 4 arguments form, but I find it a way easier not to use Inset[]at all :.

Like this :

height = 125; cb = MatrixPlot[ Table[Mod[i + j, 2], {i, 1, 2}, {j, 1, 8}] , ColorFunction -> "BlueGreenYellow" , ImageSize -> {Automatic, 2*height} ]; p1 = MatrixPlot[ Table[1, {i, 1, 1}, {j, 1, 2}] , Mesh -> True , ColorFunction -> ColorData["DarkRainbow"] , ImageSize -> {Automatic, height} ]; Graphics[{cb[[1, {1, 2}]], Translate[p1[[1, {1, 2}]], {0, 2}]}, Frame -> True] 

Not a answer

I think that Inset[] is not what you need.

Look what happens when you resize a graphic with some Inset[] :

What you need is rather a layout that doesn't change when resizing.

I can try with Raster[] if you are interested.

Interested ?

Maybe not an answer

I think that Inset[] is not what you need.

Look what happens when you resize a graphic with some Inset[] :

What you need is rather a layout that doesn't change when resizing.

Like this :

height = 125; cb = MatrixPlot[ Table[Mod[i + j, 2], {i, 1, 2}, {j, 1, 8}] , ColorFunction -> "BlueGreenYellow" , ImageSize -> {Automatic, 2*height} ]; p1 = MatrixPlot[ Table[1, {i, 1, 1}, {j, 1, 2}] , Mesh -> True , ColorFunction -> ColorData["DarkRainbow"] , ImageSize -> {Automatic, height} ]; Graphics[{cb[[1, {1, 2}]], Translate[p1[[1, {1, 2}]], {0, 2}]}, Frame -> True]