The Monitor button on an audio track is a switch (this is different on a MIDI track). You can EITHER hear the monitor chain, which includes the input of the track (monitor on) OR you can hear the playback of the recorded audio material from the hard drive (monitor off). You can NOT hear both at the same time.
That said, my guess is that you’d benefit from setting a particular preference in Cubase which automatically activates and deactivates the monitor of a record enabled track under certain conditions.
Try going to Preferences --> VST And then under “Auto Monitoring” select “Tapemachine Style”.
This will do the following: If the track is record enabled, it will automatically turn the monitor switch ON if the transport is in STOP mode or RECORD mode. If the transport is in PLAY mode it will automatically turn the monitor switch OFF. In effect, this will allow you to hear the input of the track when the transport is stopped, AND when you punch in to record, but you will hear the recorded data of that track when you “punch out” and are just playing again. Now, if the track is NOT record enabled, it will not change the monitor status at all, so the track needs to be record enabled for this behavior to function. It’s very intuitive for certain workflows… so try it (and maybe try the other settings of the “auto monitor” function and see what you like best.
One caveat I’ll add is that I can’t say for sure whether the Elements version of Cubase has this preference, but my guess is that it does.