The initial problem.
Expenses::month has data such as "January", "February", etc.
Accounts::Month is a calculaition with 1, 2, ...12 (the number of the month)
That won't match.
You could match values by changing your calculation from Month() to MonthName() but I wouldn't recomend it. If you do that records with January 2009 dates and records with January 2010 dates will both appear in your portal when you select "January" in your drop down.
One option is to filter on two pairs of fields, one for the month and one for the year. That may make your drop downs easier to set up.
Another approach is to use this calculation on both sides of your relationship: DateField - Day (dateField) + 1 and specify "Date" as your return type in Accounts::Month.
Make Expenses::Month a date field and specify this same basic calculation, but use "self" in place of "datefield" as an auto-entered calculation. You can format the field to only display the month and year and give it a calendar pop up. When you select any day of a given month, the auto-enter calculation converts it into the first of the month and that will match the calculation fields. (Make sure "Do not replace existing value..." check box is cleared).