It would help to see a picture, but in general antennas built into modules do not use the ground plane as part of the antenna. For a ground plane to be useful as a reflector, the antenna needs to be perpendicular to the ground plane. Think of the ground plane as a mirror. With a half height antenna sticking above it at right angles, it looks like a whole antenna when viewed from above the ground plane due to the reflection.
Usually the built in antennas of integrated modules are self contained. Look at the datasheets and there should be a spec about where there must not be a ground plane under the module. Some modules are arranged such that the antenna is at one end past all the mounting points so that it can stick out from the board. In any case, follow the spec about how far to keep the ground plane and other metal from the antennas.
Other than keeping the ground plain away from the antennas, the ground plane is a good thing. It is surprising that you would try to do something like this with only a two layer board. After the cost of the GSM and Zigbee modules surely the extra cost of 4 layers is negligeable. Unless you're making at least 100k of these things, trying to get away with 2 layers sounds like penny wise and pound foolish. I would use 4 layers with layer 3 being a pervasive ground plane except for where the antennas are, which should be cutouts in the ground plane at the edge of the board. Don't make the cutouts holes in the middle. This allows for putting parts on the bottom side easily.