First, to measure 380 cycles of a 3.5MHz signal (at TTL level) use Timer1 as a counter. You can preload Timer1 registers with 65157 and when an overflow is reached, either use polling or interrupts to proceed with the next step. Timer1 can read much higher frequencies than 3.5MHz.
Then, use the Hardware Uart during the counting for serial comms, just make sure you check to see if the counter overflow flag is set or an interrupt was issued.

Hope this gives you a start.

Zenon