Inverting the input and output of a UART
There is an RS232 driver chip on the board, this will be inverting the voltage levels.

Typically, a microcontroller UART will expect active high TTL level signals. A 0 is encoded as 0v, a 1 as VCC (usually 3.3v and/or 5v).

The RS232 PHY is intended for signalling over lengthy cables. It is active low and encodes 1 as -3v to -25v and 0 as +3v to +25v.

If the microcontroller is tolerant of these voltages on input pins and your UART is implemented in software then you can flip every incoming/outgoing bit (including start and stop bits). But, hardware support for this is rare.

If your microcontroller is not tolerant (and the mbed is not) then it could do harm to connect it.

The best solution is to intercept the active high TTL levels signals on the board and feed them direct to your microcontroller, avoiding the RS232 driver chip entirely.

Find the RS232 driver chip and identify its TX and RX lines. If you know the part number, find the datasheet then find the pins on the chip. If you don't know the part number, use an oscilloscope (or a continuity checker, or LED or buzzer) to identify the pins (send data from each end and look for the corresponding data line).

Once you've identified the pins, solder wires direct to your mbed, avoiding the RS232 driver chip, these should now appear at TTL levels, active high.