If correct, then the structure of that symbiotic union is part of what is passed on to the next generation, and the way that structure is passed on is not as part of the DNA specification.
I'm not sure quite how you work this out. All the information required to produce the various components for any structure you care to mention, mitochondria, chloroplasts, nuclear membranes or cilia are all encoded in the DNA either in the nucleus or between the nucleus and the discrete genetic complements of the organelles in the case of mitochondria and chloroplasts. Apart from the initial cytoplasmically or membrane inherited organelles any organelle is going to be a product of the DNA specification shared between the nuclear and organellar DNA.
Are you saying that any protein inherited cytoplasmically during mitosis is not 'part of the DNA specification'?
TTFN,
WK