What you wish to do is indeed possible. However if you do not understand this answer then you will need to get help because there is not enough space on this to do tutorials, Sorry.
Assuming that you use the Windows Mail client that comes with Windows 7, simply ensure that you have both email accounts defined in Windows Mail. You can also so this in other clients like Thunderbird.
If you use web based email then either have two web browsers or web browser tabs open at once: one logged into one of your email services and the second one into the other
T, March 2015