16. C.

An integer divisible by 15 must be divisible by both 3 and 5, meaning the unit digit must be 0 or 5.

If the unit digit is 0, the tens digit cannot be less than the unit digit, so it is not an increasing sequence.
Thus, the unit digit is 5, and the number can have at most five digits.
(1) One-digit integer: 5 is not divisible by 3, so it is discarded;
(2) Two-digit integer: 15, 45 meet the criteria, two numbers;
(3) Three-digit integer: 135, 345 meet the criteria, two numbers;
(4) Four-digit integer: 1245 meets the criteria, one number;
(5) Five-digit integer: 12345 meets the criteria, one number.
Therefore, there are 6 increasing integers that are divisible by 15.
16. If every digit of a positive integer is greater than the previous digit, it is called a "monotonically increasing integer". For example, $1357, 89$, and $5$ are all increasing integers, but $32, 1240$, and $466$ are not increasing integers. Then there are ( ) monotonically increasing integers that can be divided by 15.
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8