By definition a supply that supplies both is a dual supply. The transformer is typically the component that is shared by the two suppliesl. I would suck it up and build a dual supply: why not, they are pretty simple.
Why do you want the supply, there may be other options.
This is not a very good way as the regulators output source current, not sink it ( for most regulators ). Unless you
already have the common ground as you would with separate rectification for the two sides of the supply. A dual supply ( at least with linear regulators ) is probably much simpler than a single one with an inverting switcher ( which might count as a second supply any way ).