"script" forks a shell (or a command specified with "-c"), so I don't think you can call "script" from within the script you want to "script".
Take this (annoyingly) interactive shell script (called "fred"):
#!/bin/bash
while read -p 'Pete and Repeat were on a boat. Pete jumped off. Who was left? ' WHO
do
:
done
Run it and "script" the interaction to a file:
[myles@marklar ~]$ script -c ~/fred fred.log
Script started, file is fred.log
Pete and Repeat were on a boat. Pete jumped off. Who was left? Repeat
Pete and Repeat were on a boat. Pete jumped off. Who was left? Repeat
Pete and Repeat were on a boat. Pete jumped off. Who was left? Repeat
Pete and Repeat were on a boat. Pete jumped off. Who was left? Script done, file is fred.log
The log file contains:
[myles@marklar ~]$ cat fred.log
Script started on Mon 12 Nov 2012 11:44:41 PM EST
Pete and Repeat were on a boat. Pete jumped off. Who was left? Repeat
Pete and Repeat were on a boat. Pete jumped off. Who was left? Repeat
Pete and Repeat were on a boat. Pete jumped off. Who was left? Repeat
Pete and Repeat were on a boat. Pete jumped off. Who was left?
Script done on Mon 12 Nov 2012 11:44:51 PM EST
In short, you'll have to call your interactive shell script with the "script" command, as far as I know.