A process may send output to standard output or standard error to get it to the terminal. Generally, the former is for information and the latter for errors, but in some cases, a process may mix them up.
I'm supposing that in your case, the standard error is being used. To get both of these to the output file, you can use:
airmon-ng mon0 > file.txt 2>&1
This says to send standard output to file.txt
and to reroute 2
(which is the file id for standard error) into 1
(the file id for standard output) so that it also goes to the file.