Electric and magnetic "fields" are just mathematical representations invented by Gauss mainly in the 19th century to describe the observed behavior of electricity and magnets.
Maxwell then found out that the concept can be used to describe free moving energy, such as light and also to the complete range of rightfully named electromagnetic frequencies.
But it seems that the real "substance" that the fields describe is simple kinetic energy quanta that oscillate between the two states that the fields describe. So the "fields" do not combine, but describe the behavior of the real moving energy energy.
This recently published paper may give you more info on this relation.