I think I've found ellegant and simple solution. However, I am afraid it might be very slow for large amount of data :(

Test data with holes in sequence:

INSERT INTO MYTABLE (ID, DATE_TIME, "TYPE") VALUES ('1', '01.01.2015, 00:00:00.000', 'A');
INSERT INTO MYTABLE (ID, DATE_TIME, "TYPE") VALUES ('5', '01.01.2015, 00:01:00.000', 'A');
INSERT INTO MYTABLE (ID, DATE_TIME, "TYPE") VALUES ('7', '01.01.2015, 00:02:00.000', 'A');
INSERT INTO MYTABLE (ID, DATE_TIME, "TYPE") VALUES ('24', '01.01.2015, 00:10:00.000', 'B');
INSERT INTO MYTABLE (ID, DATE_TIME, "TYPE") VALUES ('36', '01.01.2015, 00:15:00.000', 'B');
INSERT INTO MYTABLE (ID, DATE_TIME, "TYPE") VALUES ('37', '01.01.2015, 00:20:00.000', 'A');
INSERT INTO MYTABLE (ID, DATE_TIME, "TYPE") VALUES ('40', '01.01.2015, 00:25:00.000', 'A');

The query:

SELECT
  A."TYPE", MIN(A.DATE_TIME) DATE_MIN, MAX(A.DATE_TIME) DATE_MAX,
  (SELECT FIRST 1 D.ID FROM MYTABLE D WHERE D.ID > A.ID AND D."TYPE" <> A."TYPE" ORDER BY D.ID ASC) FIRST_HIGHER
FROM
  MYTABLE A
GROUP BY
  FIRST_HIGHER, A."TYPE"
ORDER BY
  DATE_MIN

And the result:

TYPE  DATE_MIN                         DATE_MAX                        FIRST_HIGHER
A        01.01.2015, 00:00:00.000    01.01.2015, 00:02:00.000    24
B        01.01.2015, 00:10:00.000    01.01.2015, 00:15:00.000    37
A        01.01.2015, 00:20:00.000    01.01.2015, 00:25:00.000    [null]

But as I've said I am afraid that the subquery will kill the performance here.