Here is a snippet from the Arduino Reference page for attachInterrupt(). It clearly says that HIGH is on the list.
You are correct about this, but there is more to consider. Did you see this line about the Due, Zero, and MKR1000 boards right before the listing of HIGH
The Due, Zero and MKR1000 boards allows also:
HIGH: to trigger the interrupt whenever the pin is HIGH
What Arduino do you have?
In the AT328 Arduinos the external interrupt mode HIGH is actually treated the same as CHANGE.
Arduino.h defines HIGH as 1 and LOW as 0. It also defines CHANGE as 1, FALLING as 2 and RISING as 3.
The attachInterrupt() function (defined in WInterrupts.c) just does an entry of that value into the External Interrupt Control Register A (EICRA) for interrupt sense control. The only values which fit into the two control bits of that register are 0 through 3.
Table 12-1. Interrupt 1 Sense Control
ISC11 ISC10 Description
0 0 The low level of INT1 generates an interrupt request.
0 1 Any logical change on INT1 generates an interrupt request.
1 0 The falling edge of INT1 generates an interrupt request.
1 1 The rising edge of INT1 generates an interrupt request.
Please elaborate on what your program is doing. "no luck" is not a very good problem statement.