What you're calling outdoor Romex is actually called type UF (underground feeder) cable, it resembles Romex, but it's not. UF cable is THHN conductors plus a ground encased completely in PVC. Romex is a brand name for non-metallic paper bonded cable (NM-B, as printed on the jacket) with a PVC jacket. This is why type UF is suitable for burying and wet locations (or dry) where NM-B cable is suitable only for very specific dry locations.
It's rather common to protect or shield Romex with PVC in locations where (wet or not) it might be harmed by objects or people, but if you're going to be running high voltage (120 V+) outdoor lighting or receptacles it's a much better idea to just use UF, or PVC conduit and pull the THHN conductors through it as you need.
For this project you'll want to:
Have someone show you how to strip UF cable, it takes a bit of skill to do it and not damage the THHN insulation when removing the PVC casing (or your fingers in the process)
Call a utility locating service before you dig to bury the cable, it's got to go at least 18 inches in the ground depending on your location
Perhaps hire someone to trench for you if you've got long runs, or intend to just bury PVC conduit and pull your own conductors.
When using UF, please take my advice on getting someone to show you how to strip it, the folks at your local electrical supply or home center will probably be more than happy to show you. Your hands and fingers will thank you. Almost every time I was called to troubleshoot a tripping buried circuit it was because the UF cable wasn't stripped properly, and was shorting due to it.