No, Class B airspace altitudes are charted as feet above Mean Sea Level (MSL). Class C airspace is based on airport elevation, but on sectionals and terminal area charts is charted using MSL reference. Class B is described as looking like an upside down wedding cake with steps up as you go out from the main airport. Class C is typically a ring that extends from the surface to the top as charted. In addition, Class C is only active when the tower is in operation just like Class D.

Look at MacArthur Field.The top of their Class C is 4100 MSL, or about 4,000 feet AGL. Most altitudes depicted on sectionals are given in feet MSL. Ground based obstructions will show both MSL altitude and AGL height.

In the example above I noted that while they are under Class B airspace that starts at 3,000 ft MSL it is likely only 2,800 feet AGL at their location since they are about 200 feet MSL at their site.