For one, EVERYONE having headaches would be some pretty incredible odds. Especially given your spouse isn't directly related to you in any way, so the both of you having hyper-sensitivity to this sort of thing would be like winning the lottery, getting hit by lightning, and surviving a plane crash all in the same day. However, I've known of people who get headaches when the monitor refresh is less than 85Hz, even though the human eye shouldn't be able to perceive enough difference to cause headaches, and I'm prone to some right nasty buggers when the atmospheric pressure changes, so I won't rule anything out.
You might want to try and find out if your family has any sensitivity to the microwave or any 2.4GHz cordless phones you might have. You might even try plugging the airport base station in some time when no one is around, and not telling anyone. See if the headaches return. It's always possible, though unlikely seeming, that there's some flaw in your particular airport base station that's causing it to emit some sort of EM radiation beyond the wifi signal. I just can't imagine what that would be unless maybe the power supply is generating a stronger magnetic field than it should and you're sensitive to that. Even that seems iffy, since it'd require pretty close proximity, and should go away when you're outside a certain radius.
What I will say, is that so far there is absolutely no conclusive evidence that wifi equipment causes any sort of maladies like tumors. We are all bathed in dozens of different kinds of EM radiation 24/7, including radio waves from radio stations. The same sort of radiation emitted by wifi equipment, just at a lower frequency. Every time there's some sort of new technology, there's always a group of people who think it's going to bring about the end of the world. When radios were first put in cars, people though that they would be sufficiently distracting that it would vastly increase auto accidents. When the cordless phone was invented, no doubt someone claimed it would cause brain tumors. Never underestimate what a few influential hypochondriacs can do.
Ultimately, I would suggest consulting with an actual doctor to get an informed medical opinion. If you happen to be in the Chicago area, you might stop into the Diamond Headache Clinic. As the name suggests, it's a clinic specializing in headaches.