Can metal jacket wiring, that uses the metal jacket as a ground, be used with conventional Romex wiring?
If both wiring methods are allowed in your area then both can be used together.
As always, proper terminations and grounding must be considered.
Also be very careful. Even though you have AC cable, the older stuff, like what you have, is rarely an accepted or safe grounding path. These circuits cannot be extended.
The answer for these sort of questions is generally, "Ask your permitting authority". It depends on the regulations in your area.