No, there is no defined height limit to national airspace, but there is an upper speed limit to national airspace, or should we say, an interlock between speed and altitude.
Any aircraft that must generate net downlift in order to not gain altitude can be safely to be orbiting rather than flying.
And for all practical purposes, all orbital flight is considered to take place in international airspace (or in cases where the altitude is so high that the atmosphere is truly neglible, you may prefer to call it international spacespace.)
The higher the altitude and thus the further from the earth's gravitational center, the lower the speed required for a body to be considered to be orbiting rather than flying, and thus safely beyond the limits of any national airspace.