Hi Mark,
As I understand it, you have signed up for the Office 365 Home Premium and now you want to add the Outlook.com email account in the Outlook client both on a computer and a Mac. If there is any misunderstanding, please feel free to correct me.
Based on my research, the Office 365 Home Premium can be installed on up to 5 PCs or Macs. We can add the Outlook.com both on a computer and a Mac. I would like to help you, but I’m not master of this field. In our forum, we focus on the issue for Office 365 Exchange Online, Lync Online and SharePoint Online service. We have a specific channel for the Office 365 Home Premium users. Therefore, I recommend you contact them to get more professional support about the issue. They specialize in that information. Also, you can contact the Outlook.com support to check if they can provide some information for you. Thanks for your understanding.
Moreover, here is a link for your reference: http://windows.microsoft.com/en-us/windows/outlook/outlook-connector
Best Regards,
Anna Shi