There are two separate issues here.
GFCI provides a zone of protection. If properly wired, anything beyond a GFCI protective device is protected. A GFCI protective device can be:
- A combination circuit breaker and GFCI - The entire circuit is protected.
- A GFCI "deadfront" - This is a GFCI by itself which does not actually include any receptacles, though it is typically the same size as a standard duplex receptacle. It includes TEST/RESET buttons that are often switch-rated so you can also use them as OFF/ON switches. The design is that power comes in on one set of screws ("line") and goes out, fully GFCI protected, on another set of screws ("load") and everything connected to the load side is protected.
- A combination duplex receptacle and GFCI - This is what you have in your bathroom and what most non-electricians think of when you say "GFCI". Technically it is a set of screws for incoming power ("line"), which connect to the GFCI and the output of the GFCI is connected to both a duplex receptacle and another set of screws ("load"). If additional devices (e.g., more receptacles) are connected to the "load" screws then those devices are fully GFCI protected.
There is a catch: labeling. Technically speaking, for a downstream receptacle to be GFCI protected, it must be labeled to indicate that it is GFCI protected. If an inspector sees an ordinary receptacle in a place (e.g., kitchen) that requires GFCI protection and it is not labeled then the assumption is that it is not protected. Adding that label removes the doubt and solves the problem.
However, you may have another issue. Your kitchen is supposed to have at least 2 circuits that are dedicated to the kitchen and certain related areas. Your bathroom is supposed to have at least 1 circuit that is dedicated to bathrooms (multiple bathrooms can share the circuit, but they can't share it with other rooms). Older code did not require these dedicated circuits, so you may be OK, but that is something to keep in mind. In particular, you can't make things worse. So if you want to add any new receptacles to your kitchen or bathroom they should be on circuits dedicated to those rooms, and you also shouldn't add receptacles elsewhere (e.g., garage) on the existing circuit.