Yes, this is possible. When setting up the visualization you need to end up with a configuration like this (specifically note the boxed area):
To achieve this, first choose "Split Chart" under "Select buckets type". Then make sure the "columns" button is clicked. Then setup the aggregation for the broader grouping (months, in your example).
Next, click "Add sub-buckets" and choose "X-Axis". Then setup the aggregation for the narrower grouping within each broader grouping (i.e. each of the bars within each month, in your example).
Finally, click "Add sub-buckets" again and choose "Split Bars" (the only option). Then setup the aggregation for the stack colors (group A, B, C, in your example).