Ahhh okay. My mind had catalogued it to mean death.

In common use ("don't be morbid", "that's morbid") I agree that 'morbid' has a connotation of death, so I don't think your understanding is wrong. In this case, a 'co-morbidity' is a term of art in the medical literature with the specific meaning of "occurring with".

Hence’s the CDC’s “Morbidity and Mortality Weekly Report”