Depending on your definition of "commercial availability" (it is pretty unavailable to me) Phase One AchromaticPhase One Achromatic might fit the description.
One more comment: the relative intensity / sensor sensitivity (it ends up the same) of visible and invisible light differs greatly. Getting the exposure in invisible light right is more art than science (in my experience - near UV is about about 4 stops off, and near IR about 5, but a lot of bracketing is required).
Using filters and separating the three (UV, visible, IR) shots allows for longer times / wider aperture for the invisible light ones. Shooting with the same settings as for visible light would result in a dark image.
Combining all three spectrums in one image would in most cases lead to the visible light image "crowding out" the two invisible ones.