R.J.
My recommendation is to call your doctors office, tell them your H is freaking out about the aspirin from what he read online (or blame a MIL, and he'll get fewer sighs and more tolerance)... and ask for them to talk to him &/or you about why the recommendation was made.
LOTS of things (especially medical things) don't sound like a good idea online. And that's if you've got correct information. Incorrect info compounds the problem.
So take the correct info: It's not a good idea to take aspirin as a PAIN RELIEVER (which is the qualifying phrase that gets ignored) while pregnant. It gets skewed 6 ways from sunday. But the bottom line is because of the risk of miscarriage.
Now take blood clots. One of the most common ways to get them is to fly on an airplane (esp coach). Blood clots also cause miscarriage. And death or brain damage to the mum (depending on where the blood clot terminates) is a strong possibility as well.
Add the two together.... and you've got a risk assessment.
It's like being in a house that's on fire. Do you run outside without shoes on (and risk cutting your feet, or falling and breaking your neck, or getting hit by a car)... or do you stay nice and safe in the house and protect your feet & your neck and burn to death? Nope. You do the risk assessment, and decide to leave the burning house. But you go out the window (which is not recommended) and slide down the roof (which is not recommended) and jump (which is not recommended UNLESS situ a) house on fire, or situ b) escaping a burglar/rapist/ etc.
In normal every day life you don't take aspirin when preggers. But the safest thing to do when flying is to prevent blood clots. So you go out the window, and over the roof. Because in THAT situation, it's the smart thing.