Hi

You cannot use your current PS With both 78xx and 79xx
Because the 0v line of the 78xx is the 0v line of circuit
and the 12V(or whatever) of the 79xx is the 0V line of the
circuit.
The solutions are :

1) you can use a center tapped transformer and create +12v/0v/-12v, and it'll be easy.

2) you can use highher voltage(x2) and create a virtual
ground between the 78xx and 79xx by 2 capacitors connected
from the +v to the 0v, in series, and use the middle point
between them as the 0v

Goodluck
OK