Which process of genetic recombination involves genes from both parents?

The process is called Fertilization.

The process of Fertilization is the fusion of the gametes for the development of a new organism. The process involves the fusion of the ovum from the mother and the sperm from the father. This is where both genes of the parents combine in development of a child.

Both of them have a nucleus, golgi apparatus, cell membrane, smooth and rough endoplasmic reticulum, lysosome, and ribosomes.