Your internal audits should be process audits. You seem to be differentiating between the two, so if you could explain what your IA audit checklist looks like, and what your process audit is expected to accomplish, we'd have a better idea of what you're asking.
According the TC 176 Auditing Practices Group, checklists are just one tool in the auditor's tool box (that might be a direct quote, but not sure). Depending on how loosly you define the word checklist, you can still do a process audit with a checklist. I use something very close to a turtle diagram, but still call it a checklist, as I also include direct questions from the documented procedures.
As Jim said above, what are you calling a checklist? If your checklist is from the standard alone, then it won't contain elements of the process and will probably be pretty much useless.