All the UPS's I now work with are switching type. The input is fed right thru to the output(with a little going to charge the battery) untill an over voltage or under voltage condition is sensed. That condition is usually one that exceeds +/- 10 percent of the normal 120VAC. If the voltage drops below about 108VAC, the unit switches to the battery powered inverter and disconnects the input power from the load. This is typical, but some come set with higher tollerances, or can be switched to higher tollerances if desired.
If not overloaded the inverter output should provide 120VAC. This switching occurs very fast(usually less than 1/2 cycle of 60HZ). The UPS continues to monitor the input power and when it returns to within specification, it re-connects the input power to the load and resumes charging the battery. I have 3 ups's in my home. One for the entertainment center, one for the computer and one for the pellet stove. They are great for short power failures and for momentary generator overload conditions. I only have 3KW available from my generator, but my largest load is also only a 2/3HP well pump that dosn't run very often. I will occasionally overload it though, and the UPS's protect the expensive equipment while this is happening. The Beeping UPS is also good for bringing my attention to an overload condition that I might otherwise be unaware of while on generator power.
If you are taking power drops down to 95VAC, your generator is too small to deal with your surge loads. This is especially true if they last long enough to see on a kill-a-watt meter. Your generator is probably fine for most of your normal emergency loads. My house on backup power typically pulls less than 2KW. That big pull from your furnace startup, or a combination of loads is pulling the voltage down too low. Get a bigger generator, reduce the load to within the capabilities of your existing generator, or put the critical items on UPS's. I have done the latter 2 of these to live comfortably within my 3KW limit.
To the gentelman who lost a computer power supply when the UPS exhausted it's battery, I would say you have a bad UPS. The UPS should have shut itself down when the inverter was no longer able to maintain rated output, just like it disconnected from line power when it was not receiving correct voltage from that source. Another issue could also be caused by a cheap UPS. A cheap UPS is probably not going to give a real good sine wave output. Switching power supplies such as those found in computers do not like square wave or modified sinewave outputs.