It’s your story and you should decide how the characters fit into the plot, but I’ll try to help you on your way of thinking towards a solution.
First: what’s the story about? It’s not a job interview. It’s fiction, there has to be a conflict between the two characters, one wants something and the other stands in the way.
The second step is to think about which two characters can make this plot stronger (and that is the answer to your question, as they have to be different to make the story interesting).
Let’s say the doctor is aggressive, ambitious, as his vampirism isn’t something quiet and peaceful and abuse doesn’t contribute either. So the first thought would be that the mortician could be quiet, modest, whispering rather than speaking and never raising her voice, buried in thoughts and shy. Would that make a story?
Let’s imagine that the mortician has access to the cure the doctor is looking for. He tries to force her, charm her, use every trick in the book to get what he wants (aggressive, ambitious) but this has the opposite effect on the mortician, as she closes up and runs away from this horrible man. So the doctor has to change or walk away, a choice that he will make at the start of the story and will change in the end or at the middle (when he has to find a better way to work with the mortician).
This way, the story has a plot-side (the cure) and a character-side (the relationship between two opposite characters should change and improve to solve the problem). That’s a solid foundation for a story, something you can work out.
I hope this helps.