What you describe is what Windows is supposed to do, but often users complain it doesn't,
Windows should remember the last size that application windows were resized to, but it seems the coding is a bit flaky there. We often see users who maximise a window, but the next time they open it, often after a reboot, it opens smaller than maximised. We then go through hoops and loops to get it to stick.
I don't see any easy way for you to achieve what you want. There is no readily available setting or option to change, and the only method I can suggest is to minimise the window you want to temporarily lose focus on, work on the other one, then retrieve that first window from the Taskbar.
Or perhaps the easier way is to always use the Taskbar to call into focus the window you need.
But I suspect neither is satisfactory for you because we all have our own preferred ways of using Windows. So, not much help from me I fear.
I use Interent Explorer 8.0 on Windows 7-64bit and I most often, don't use the "full screen" format but just a regular looking size window so I can have other apps open beside it or partially behind it.
Occasionally, I need to refer to what is on another window to copy stuff to something in Explorer so I will "temporarily" resize my Explorer window down a bit. But after that, it seems like it takes forever for Explorer to reopen to my default window size. It keeps openning to the smaller window frame which is very iritating. What is the quickest way to teach Explorer to maintain a default window size?