naturally any of such tricky programming need to be done very carefully.

E.g. if the subroutine remove a byte from the buffer, it must watch, that at the same time the interrupt part can place the next byte into the buffer.

Also you must watch, that the subroutine was not entered to often. E.g. you can set a bit, during the subroutine runs:

org 23h
        jmp    sio_int
...

sio_int:

...

        jb     sub_runs, do_reti
        setb   sub_runs 
        call   do_reti

....

        clr    ea
        clr    sub_runs
        setb   ea
do_reti:
        reti

Peter