Dang you Missouri. I lived in Columbia. It didn’t feel all that progressive, but I guess it was progressive for the state. 
Asian (in case my reputation doesn’t precede me around here) born and raised in Southern California in semi-affluent suburbs surrounded by Italian and Mexican Catholics, Welsh Mormons, Scotch and Irish protestants, Israeli Jews, Greek and German Orthodox Christians, and who-knows-what other neighbors of western European ancestry. We were all just mainstream people living in mainstream America.
When I first went to Grand Junction, Colorado to visit the [Caucasian] woman who is now my wife, she offered to take me out to dinner with her kids and the kids chose a nice family diner – something like an up-scale Denny’s restaurant. When the waitress first arrived at the table, she asked, “Do we need separate checks?”
I had somehow learned old-world manners in which the male always pays (that’s a different thread somewhere around here), so I shook my head and said, “No. I’m buying.”
“No you’re not.” my host told me. She had learned a different protocol and explained, “I invited you, so I’m paying.”
I looked at my host, at the kids, at the waitress, realized everyone was staring at me and the time was not right for an argument, then simply smiled at the waitress and nodded, “In any case, one check will work fine.”
“Okay.” she nodded, “Drinks?”
After the drinks were requested the waitress went away and it was the 9-year-old daughter who complained that the waitress didn’t seem to think we were together simply because I look different.
Another interracial incident that sticks in my memory occurred decades ago when I was in college. My girlfriend at that time, who was very proudly Scotch/Irish/Welsh, never pursued anything past high school. However, when she came to visit me on campus one day there happened to be a bazaar along the main courtyard and we went browsing among the booths. She stopped at one booth and said, “Buy me a ring(?)” and I looked at the stuff on the table and saw that they were simple gold electroplated trinkets selling very cheaply. She picked one out and a black man came over to write up a little receipt. While I was fishing in my pack for my wallet, he casually asked, “So what’s it like to be an interracial couple on campus?”
Since my girlfriend wasn’t a fellow student I didn’t consider us to be an “On Campus” couple. We were not regularly seen as a couple there because our regular activities simply occurred elsewhere (San Diego is a huge town with lots of places to go and things to do well away from the colleges). So as I pulled out my wallet and handed the man some cash, I frowned and said, “I dunno. Why do you ask me?”
The man frowned back, swapped the bills in my hand for the receipt he had just written and said, “Have a nice day.”
My girlfriend and I wandered off toward the library. Suddenly she stepped in front of me, turned, put her hands on my shoulders to stop me, and announced, “I’ve got something important to tell you.”
“Uh, what?” I asked, somewhat surprised by the confrontational tone and more surprised that she was stopping our walk.
“You may not have noticed.” she continued, “But I’m white.”
It still took me a minute to realize how my self-image and all my social assumptions completely failed to correspond to the ring vendor’s expectations. And then we just laughed all the way to the library.
–G!
Biologically, we are all one RACE 
Also live in Georgia, and am the white half of an inter-racial couple. He’s AA and lives in Florida. We are both in our 50s, have jobs that involve alot of travel, and we have dined and stayed in many places across various states.
We’ve never been asked about separate checks in Georgia, Florida, or anywhere else.
Maybe I am giving off a vibe as a chick who would never pay for her own meal?
I’ve got to get me one of those. Somehow I’ve got the vibe that gives the impression that says I will pay for everything.
My wife and I, both women, are frequently asked if we want separate checks in non-business meal contexts.
Hijack: Two of my housemates have been married for nearly a year now. They still haven’t bothered opening a joint account. Their marriage license is stuck to the side of the fridge with a magnet, and their bulletin board still has post-its all over it that say, “reception???” They MAY get around to throwing the party this fall. 
They were de facto hitched before but had to get an official to write it down for insurance reasons, so that probably contributed.
On topic: Others have suggested it’s because you’re in tourist areas, but you also might be in… less-affluent ones, I suppose? Not necessarily low-income, but where individuals don’t necessarily have scads of extra money on them at all times. My own experience is that if you look like a college kid, and are in a college town, and are eating at a place where college students collect, they will ask you if you want separate checks even if you’re practically groping each other. They are perpetually unsure whether any one of you can pay for the whole table, and have probably learned from experience that making a load of humanities majors do long division by themselves would just be painful. That wouldn’t be the reason they ask YOU, if you don’t look like a lost 19-year-old, but it might be habit if they ask a lot.
And the women as accesories to the men, which for you guys goes in the same direction but for Broomstick ran in opposite ways. In the OP’s case, the assumptions are again opposed: woman is accesory to man, but darker is accesory to lighter. Out for lunch with white coworkers in Philadelphia we weren’t asked about separate checks; with a male black coworker, we were asked but then, I also was once asked if he was bothering me and had to remind myself that slapping cops is illegal (there was absolutely nothing about our interactions which looked like “bother”).