I almost had a similar experience with an 87 Suburban that I used to drive. One of the axle seals blew out on my commute home from school (about 25 miles), and axle grease was sprayed on my hot brakes. I noticed smoke coming from the car so I pulled over into a gas station. While blankly looking at the truck trying to decide what to do the grease managed to seep its way into the drum, and proceeded to catch fire. Luckily there was a hose nearby, and I backed away and doused the flames before any damage was done. Drove it to a nearby repair shop, had the axle replaced (it was damaged from driving without any grease), and had it back the next day. It is good that you and your family are okay.
1976 300D (W115) - 330K and still going (sort of)
1991 300D 2.5 Turbo - Sold at 221K
1983 280SEL - Sold at 206K
1981 300SD - Sold at 232K