Se intendi il set delle date di inizio e di fine, quindi inseriscile in una colonna:
WITH t AS (
SELECT invoice_no, invoice_start_date, invoice_end_date, check_date, status_code,
FROM INVOICE_HEADER INNER JOIN
INVOICE_HEADER_CUSTOM
ON INVOICE_HEADER.invoice_id = INVOICE_HEADER_CUSTOM.invoice_id
WHERE status_code <> 'REJECTED' AND
Check_Date BETWEEN CONVERT(DATETIME, '2014-12-01 00:00:00', 102) AND
CONVERT(DATETIME, '2014-12-31 00:00:00', 102)
),
t2 as (
select d, row_number() over (order by d) as seqnum,
count(*) over () as cnt
from (select invoice_start_date as d from t
union all
select invoice_end_date as d from t
) t
)
select dateadd(day, datediff(hour, min(d), max(d)) / 2.0, min(d))
from t2
where 2 * seqnum in (cnt, cnt + 1, cnt + 2);
