If you are on a BIS, emails that you send from your BlackBerry will not automatically show up in the email client on your computer.
If you want them there, you can log in to your BIS and add your email address as an AutoBCC. If you do this, you probably will want to also set up a filter with your email address so the messages don't get pushed back to the BlackBerry.
And note that the messages will go to the Inbox of your email client. You will need to move them manually or with a rule.