Just so you know, HDPE = High Density Polyethylene. PEX = Cross-Linked Polyethylene. PEX is a modified version of HDPE where the polyethylene molecules are cross-linked (by one of three methods) during the manufacturing process.
PEX is stronger and more flexible than HDPE, making it ideal for plumbing inside a home where you need to make fairly small-radius bends and where you need extra safety against pipe failure. PEX can also be used in exterior applications (either buried or enclosed in an outer covering, because it is not UV resistant). The reason HDPE is often used for buried water supply lines is primarly due to cost: PEX is more expensive than HDPE. For a buried supply line (which is usually a relatively straight line, or where the bends can be of very large radius), the greater strength and flexibility of PEX do not justify its increased cost. That said, I believe the cost of PEX has been decreasing as the scale of PEX production has increased dramatically in recent years. So PEX may be more price competitive now than it was in the past.
Moles typically burrow within the top 12" of the soil. You will need to check you local code for proper depth of burial, but I wouldn't go less than 18-inches. Also, I recommend backfilling with a layer of sand covering the pipe: the sand will protect the pipe from rock damage, will deter rodents, and will make it much easier to unearth sections of the pipe if you ever need to make any repairs. You may want to put a protective sleeve around the pipe where it transitions up out of the ground to help protect it from varmints and other possible sources of damage (like shovels!); that sleeve can be Schedule 80 PVC.
Don't forget to have the installers lay a tracer wire with the pipe. And it's a good idea to run a blue-colored plastic utility marker tape (like
this one) in the backfill over the pipe (above the sand layer).