I'm not sure whether that is possible.
It may be more convenient for you both to share the same account and AdobeId;
that would simplify use of the single computer with single ADE instance, and would also mean you could share books.
In Windows, you can take advantage of the registry export function if you have two or more Adobe Digital Editions accounts but only one PC. The following applies to Windows XP. I'm not familiar with later windows products. It is not necessary that you use an email address for the ID and it isn't easy to change the ID should you get a different email address.
Be very careful while using regedit. A mistake can have dire consequences. Changes made in regedit take effect immediately with no way to undo the change other than to change it back manually.
With Adobe Digital Editions authorized for one of the accounts:
Click Start, select Run (or simply press the 'R' key), enter regedit and press the Enter key.
Right click Adept key and select Export.
Select an appropriate name (it can be changed later) and folder location, perhaps the Adobe Digital Editions folder. The exported registry key file will have a .reg file type. Do not change that.
Now, from within Adobe Digital Editions, press Ctrl-Shift-D, erase the current authorization and authorize using the next ID and password. Once the new user authorization has been accepted export the new registry key. This can be done with Adobe Digital Editions running. Use a different file name of course.
To switch user authorizations, double click the exported registry key file for the desired user. This can be done while Adobe Digital Editions is running. I've added shortcut entries to my Start menus to make it easy to switch between my two accounts. You can click and drag the exported files to the desktop to create clickable icons.
If you download and add DRM protected ebooks from two different accounts to a common PC using Adobe Digital Editions, you will only be able to read ebooks authorized for one account at a time on the PC. You also must ensure that ADE is authorized for the proper account when downloading ebooks for ereaders. This can be checked by selecting Help, i (or Ctrl+Shift+i). Multiple accounts do cause inconveniences.