Well, there are two kinds of physical outputs on televisions, and there are two audio types of outputs, and I'll explain each of them.
The headphone jack is one option to connect headphones - most televisions have them, but some (particularly larger sizes) do not. This would be the 3.5mm connection, like those found on a portable mp3 player. Those will cut the sound to the TV speakers as you mentioned.
The auxiliary jack - if used - will not cut the sound. Those are the red-and-white RCA jacks. Not all headphones have an adapter, and an amplifier - either in the headphones or connected to an amplifier - will be how you adjust the volume, since the audio from the RCA ports is fixed - meaning, you can't change the volume, and the amp will not be loud enough on its own to power headphones.
In this situation it is entirely possible to get the result you want, however there may be extra equipment necessary. If that's an option, then let me know which models you're considering and I'll see if we can match up the features to help you out.
For instance, a small portable radio may have an AUX (RCA) input, and you could plug the headphones into the radio's headphone jack and manually adjust the volume on the small portable radio as loud as your father would like it, while the television's volume for everyone else would be controlled by the remote and come out of the television speakers. Does that make sense?
My father is hard of hearing, so likes to use headphones. But my mother wants to watch the TV at the same time. So he can't use conventional headphones in the headphone socket , as this stops all other sound. He needs a TV with an audio output jack so he can use special headphones and not affect the rest of the sound for my monther.
I am finding it impossible to tell on line which TV's are suitable. None of the product info seems to describe whether the tv has the oudio output facility - or am I looking for the wrong description? Perhaps it is called something other than "audio output"?
Does anyone know?