One bad bulb would not make both headlights nonfunctional. Two bad bulbs could, of course, but having both high beam and both low beam filaments go out at the same time seems very, very unlikely.
Besides the headlight switch, it might be worth checking the dimmer switch and its connections. Also, if you have daytime running lights, they sometimes use the same bulbs as the headlights and a faulty relay or something in that system could cause problems. (Sometimes daytime running lights use their own dedicated bulbs, or the parking lights, or perhaps even turn signal indicators rather than the headlights.)