With dual filament bulbs (like H4, HB5, H13, etc), the low beam filament will drop out when the high beam filament comes on. It will kill the bulb to have both filaments running at the same time.
With dual bulb setups (like HB3/HB4 or H9/H11), the lows sometimes stay on with the highs, but it's manufacturer dependent. I don't believe either implementation is required or disallowed by FMVSS 108...it can work either way.
Our Acura has HB3 highs and H11 lows, and the lows stay on when you switch to the highs. If the fog lamps are on, the fog lamps go out when the highs come on, and come back on when the highs go off.