Do we apply separately for the DTV visa as a married couple or is there a joint application process?

You should never purchase tickets until your visa application is approved That's rule number 1 and immigration of every country states that . For a spouse ti apply they usually do after the original person applies they do as a dependent. Its easier to do individually and doesnt effect either application. But both application process are a personal choice people have previously done both. You can search in this group for previous posts