Interrupt triggering communication with a host computer and counting interrupt calls

I'm planning to use an interrupt pin (INT A) to trigger the start of a control flow diagram for a trial. Once the trial is triggerred, the microcontroller would communicate with a host computer. I was hoping that I can use the host computer to count the amount of times the signal on INT A is triggered, while I'm serving the interrupt service routine. How much complication am I running into? Would it be strongly recommended to change my design on how I use the microcontroller and other circuit to perform the task that I want (hopefully I'm not too vague about what my task is required to perform)? Thanks in advance.

Thats a common technic used to trigger a certain device.

Counting number of times the external interrupt has occurred & after doing the operation controlling part.

If the external interrupt count below (<) the set counter it must turn off (Clear) the counting register within a calculated time.