What mikeone suggested is one of your options. And in that case you can have just one account set in Aquamail for your Gmail account, and two identities (the second being your business account user@domain.com).
In that case, all you incoming and outgoing messages would be going through Gmail's servers.
Alternatively, you can set up an (additional) account in Aquamail, where IMAP server would be set as Gmail's IMAP server, and SMTP server -- one for your company's (as that seems to be working, - and that's what you seem to be using in your desktop's outlook). In that case, you don't need to set up the alias in Gmail, as all outgoing e-mail will be handled by your company's server.
For that, - in Aquamail, start adding a new account, and choose "internet/IMAP" (not GMAIL!) account. Choose "configure manual", and enter: imap.gmail.com Requires SSL: Yes Port: 993
Specify your gmail login/password.
At the next screen, for the outgoing messages, specify your company's SMTP server's settings and your login/password for that server.
Note, that in the scenario (1), you'd want to configure not to save a copy of outgoing messages to "Sent" (as it is done by Gmail's server automatically). And I believe, that's the default setting for Gmail accounts in Aquamail.
In the scenario (2), you'd want to configure saving a copy of the Sent message in "Sent" and make sure it is configured to sync with "Sent messages" of your Gmail account. (Read FAQ for details on how to do that.)