First of all, welcome to the community! I hope that you’ll find your time here to be positive!
As to the issue that you’re encountering, I believe you’re seeing an effect called “Z-Fighting”. In essence, the two surfaces are so close together that the measure of which is closer to the camera–and thus which should be drawn over the other–becomes unreliable, causing regions from each to be drawn.
One solution is to apply a “depth offset” to the NodePath of one of the objects: a value that slightly alters the measure of the NodePath’s distance from the camera, thus allowing it to be “separated” from other NodePaths that are at much the same distance.
This does require you to know which objects should be rendered over which, of course.
For details on setting a depth-offset, see this entry in the API.