avast! supports multiple accounts. The default account is just that default (not only account). That is the one that would be used if for instance you wanted to send a file from the virus chest to avast team.

Set up your second pop3 account within Thunderbird as if avast wasn’t there, just like your other account is set up.

The latest version of the Internet Mail provider is transparent so no more messing with the ini file to get it to work.