A cross-[What] kind of romance?
In the scientific taxonomy of Living Things, you have:
etc. down to Species, and maybe thence to Breed.
If I were talking about my neighbor's dog who is half Chihuahua and half German Shepherd (no she is, really), I would say her parents had a "cross-breed romance." (they are both of the species Canis lupus familiaris)
If I were talking about a mule, I would say the mare and the male donkey had a "cross-species romance." (they are both of the genus Equus)
And so on and so forth up the improbable chain. In a science-fiction setting, you can cross a Vulcan and a Terran and have a viable hybrid child, even though they come from two different planets and shouldn't even share a Kingdom, let alone enough genetic similarities to breed.
But what's the "cross-" when you have a romance between biological life and non-biological life? For example, if Star Trek: Voyager's Seven of Nine and the Emergency Medical Hologram had actually had a relationship? Or when Data dated Jenna D'Sora (TNG's "In Theory")? (The Holodoc is a software-based lifeform; Data is a hardware-based lifeform.)
I am establishing such a romance between two characters, and I've no idea what to call it. (Of course, figuring out what to call it may wind up in dialogue as part of establishing it, because they don't know what to call it either.)