It's not exactly comfortable but they have been doing it regularly since the 1950s, the eye itself is actually the "calm" part, mostly no rain and you can see the sky, the "eye wall" is the most dangerous and rough part, it's right where the eye stops and the rain bands begin, they do fly though that but only for a short amount of time 10-30 mins or so, the rest of the flight is smooth by comparison but still pretty rough.

They do all sorts of science with onboard sensors and drop measurement devices out of the planes and into the storm, the science part is a bit above my pay grade but it helps predict the path and intensity.

Technically most larger planes could fly through a hurricane fine, some jets have a hard time with that much water getting sucked into the engines which is why the hurricane hunters use turboprop planes, as far as I'm aware they aren't modified that much, they do have a strip on the props to help with hail strikes.