Is there any way to do an MDX query with a start/stop filter specified in days, but aggregate results by month?

For example, if the user specified a date range of Jan 15, 2005 to April 14, 2005 and an aggregation level of "month", the expected results would be four rows:

January (only contains data from the fifteenth to the thirty first)
February (data for entire month)
March (data for entire month)
April (only contains data from the first to the fourteenth)

I can filter by month and aggregate by month:

Code:
SELECT
	[Date].[Month].[2005-01]:[Date].[Month].[2005-04] ON Columns
FROM [My Cube];
I can also filter by day and aggregate by day:

Code:
SELECT
	[Date].[Day].[2005-01-15]:[Date].[Day].[2005-04-14] ON Columns
FROM [My Cube];
But I don't know how to filter by day and aggregate by month. Is this at all possible using MDX?