@mhoran_psprep is exactly right with "In a resume/CV include all jobs that will help you get the job you are applying for. You are selling your experience." I also agree with his cautions but wanted to put a different perspective out there.
Do qualify your role, and the dates, I would expect to see something like:
- a header for the company that is your full time work (dates of employment, company, current title), including the note that you are a full time employee.
- a header for the company that is your part time work (same structure as the previous bullet), including the note that you are a part time employee.
- a clear description of the work in each one. If you get something noticeably different out of these two jobs, make sure to spell out what is relevant. For example, I could see it being a nice thing if the part time job pays a lot less but gives you a greater sense of ownership or more ability to take risks or extend your skills.
Be ready to speak to it. If I were your hiring manager I would probably be asking myself - "why is this person working two jobs??"... is it that...
- The full time job doesn't pay enough - understandable if this is a low-paying job, but if we're talking something in high demand like software development, this is harder to believe unless there's a debt-inducing skeleton in the closet.
- The person is bored. If the person is bored... why? is s/he slacking in one of these jobs? Is s/he underutilized?
- Also - how does this candidate recharge? And does s/he get enough sleep/food/life time? There's no universal truth on this, but I don't know very many people that REALLY can work two jobs continuously, one full time, that are largely similar (same field...) without burning out in a year or two.
- Do both employers know about each other? It's a big difference if the person is working two jobs because s/he was able to pick up some extra cash consulting for two companies in a partnering relationship where presumably they can compromise on deadlines and timing.
- What happens when there is a conflict of interest between timing? Are both jobs really such smooth sailing that this candidate never has to choose between missing deadlines?
I'd definitely be asking variants of these questions to you as a candidate. Some I could pose point blank -- "Why two jobs at once?", or "How do you recharge?" some I would probably pose from an experiential standpoint - "what happens when you have conflicting deadlines or urgent work in both jobs?".
Mileage varies significantly between industries. I know tons of people in the performing arts who have two or even 3-4 "jobs" - all in their chosen industry - as different artistic groups have different schedules, rehearsal expectations, etc and there can be enough fluidity in membership to accommodate schedule conflicts.
I've also seen cool stuff like engineers who also work as adjunct professors for their brand of engineering - both relate to skills in engineering, but there's a noticeably different pattern and pace. And adjunct professors can often plan their class schedules to fit with other job demands.
But the hard areas are often stuff like "knowledge work" where the time required to get something done is very hard to predict, and there's an assumption that brilliance could hit you at any time and that you'll work at least some weeks with a high number of hours to meet important deadlines when the project is in crisis. These areas can also have heavy intellectual property concerns.