The electron and heavy hole energy levels of two vertically coupled InAs hemispherical quantum dots/wetting layers embedded in a GaAs barrier are calculated numerically. As the radius increases, the electronic energies increase for the small base radii and decrease for the larger ones. The energies decrease as the dot height increases. The intersubband and interband transitions of the system are also studied. For both, a spectral peak position shift to lower energies is seen due to the vertical coupling of dots. The interband transition energy decreases as the dot size increases, decreases for the dot shapes with larger heights, and reaches a minimum for coupled semisphere dots.