To be more specific, is the question how much you can discharge the batteries before you have to recharge them (start generator) or when turn on the charger when you have hook ups?
Advanced inverter/chargers sense charging diagram automatically and will come to maintaining stage and the best you can do is leave it on permanently.
When it comes to deep discharge the voltmeter is not precise as it will change the readings depends on the load.
I have load tester that allows me to test the battery stage and I have seen youtube video about new technology gadget where pocket-sized instrument runs series of test to tell you battery state. I am skeptic about new gizmos, but it looks good on the picture.
Precise instrument would be one of those

But than who wants to mess with acid?