The potential properties arising from the interaction of semiconductor quantum dots with electromagnetic fields have been studied intensely in recent years for their applications in nanophotonics and quantum technologies. The asymmetric double semiconductor quantum dot molecule is a semiconductor quantum dot nanostructure that exhibits unique optical properties, leading, for example, to important quantum optical phenomena like tunneling induced transparency, Autler-Townes splitting and slow light generation without the need of an external electromagnetic field. When semiconductor quantum dots and metal nanoparticles are placed close to each other, with distances in a few nanometers range, coupled nanostructures are created that have, in many cases, enhanced optical properties in comparison to the individual semiconductor quantum dots and metal nanoparticles. Recently, attention has been given to the optical properties of a coupled nanostructure fabricated by coupling a metal nanoparticle to a double semiconductor quantum dot molecule. In the present work, the behavior of the absorption and dispersion properties of the double semiconductor quantum dot molecule in the presence of a spherical metal nanoparticle is explored. Specifically, tunneling induced transparency, Autler-Townes splitting, and slow light generation are obtained in the semiconductor quantum dot structure under the presence of the metal nanoparticle and their properties in the interparticle distance between the semiconductor quantum dot structure and the metal nanoparticle is studied.