You don't see a pulldown in the From field showing the two accounts when you compose a new message in Outlook 2011?
If not, that's an issue best taken up with Microsoft Support.
Mail in Mac OS X has a similar "from" pulldown you use to choose the account from which the message should be sent. I haven't tried it with two Exchange accounts, only with one Exchange account and three POP accounts, but I don't see any reason why it would work with two Exchange accoints.
Thanks for the reply.
The problem is I have my Exchange account linked to my Work and Personal accounts. So work and personal come into one mailbox on the Exchange server.
Doing it this way means I only have ONE account in Outlook but that one (exchange) account manages two of my accounts.
Now, in Outlook 2013, it allows me to choose which of my linked accounts I want to send from but in Office 2011 it does not.
For now I've moved to Apple Mail which allows you to add smtp servers manually and pick which one to use for emails being sent so that works for me at the moment.
I can only assume the Microsoft will fix this issue in a later version of Office for Mac.