I don't think that it's supported-whether it's possible in lore for a half-vistani to be born a caliban or not is irrelevant.
That is true, but mechanics aside I am also unsure whether it is possible to be born both half-Vistani and caliban as I have never heard of one. For the sake of the arguement let us assume it is.
The Lunatio or Moon Madness occurs when someone is only a half-blood Vistani. Caliban are mostly just deformed humans, they're not truly an entirely different race or anything, so whether you are a human or a human caliban would probably not make a difference in this case as long as half the blood in your veins is Vistani blood. However, if your caliban is less than a half-blood Vistana (like a quarter or 1/8th Vistana) you would not be affected by boons and curses of being a half-Vistani regardless.
Most caliban are also pretty unlikely to end up forming families of their own, so this character would most likely have to be a brother, sister, cousin or child in relationship to your character then.
That is as much as I can tell you on the matter, mostly using common sense. This is probably largely unexplored territory, the question is more whether a half-Vistana caliban is possible at all.
I am actually not even sure if half-elf calibans or any other combination of half-blood calibans exist either, so I would suggest trying to find some canon information or a DM ruling on that first.