I might very well be totally of but I believe you are just missing COALESCE
SELECT c.*,
COALESCE(SUM(CASE WHEN billtype = 1 THEN total ELSE 0 END), 0) totalpaid ,
COALESCE(SUM(CASE WHEN billtype = 2 THEN total ELSE 0 END), 0 totalowed ,
COALESCE(SUM(total), 0) AS totalbalance
FROM
tbl_customers c
LEFT JOIN tbl_customers_bills b
ON c.customerid = = b.customerid
and billtype in (1,2)
GROUP BY
c.customerid
From the MySQL Reference
COALESCE(value,...)
Returns the first non-NULL value in the list, or NULL if there are no non-NULL values.
mysql> SELECT COALESCE(NULL,1); -> 1
mysql> SELECT COALESCE(NULL,NULL,NULL); -> NULL