Use of SUM and COUNT with GROUP BY

All,

I have a set like below:

State   DOB           StartDt         EndDt           Desc      Category MemberID     SubID   Code
NC      2003-01-30      2014-01-01      2014-01-31      Child        B     123456       2       38
NC      2003-01-30      2014-01-01      2014-01-31      Child        B     123456       2       39

NC      2003-01-30      2014-02-01      2014-05-31      Child     B        123456       2       38
NC      2003-01-30      2014-02-01      2014-05-31      Child        B     123456       2       39

NC      2003-01-30      2014-06-01      2014-07-31      Child        B     123456       2       38
NC      2003-01-30      2014-06-01      2014-07-31      Child        B     123456       2       39

NC      2014-01-17      2014-01-01      2014-07-31      Infant       S     456789       1       49
NC      2014-02-04      2014-02-01      2014-07-31      Infant       S     246376       3       49

-- MemberID and SubID identify 1 member
-- Member 123456 has 2 distinct "Code" i.e. 38,39 but each code has different "StartDt" and "EndDt"

-- Expected Result

State   Desc      Category      CountOfDistinctCode                     TotalMonthsEnrolled
NC      Child      B            2 (38 and 39 for same member)           7 months (1 + 4 + 2) (Difference between StartDt and EndDt:1 (1/31/2014 - 1/1/2014) + 4 (5/31/2014 - 2/1/2014).. )
NC      Infant   S              2 (Same code 49 but different member)   13 months (7+6) (7/31/2014 - 1/1/2014 = 7 months + 7/31/2014 - 2/1/2014 = 6 months)

I tried doing a count of distinct Code and the summing up the member months, grouped by State, Desc, Category, but I am not able to get 2 and 7 for child, it somehow calculates Months as 14 (7+7). Please let me know what you guys suggest.