Burying AC, solar DC and ethernet cable
For networking, use fiber optics, or point-to-point wireless.
By the time you provide adequate lightning suppression (UL497 Primary Protection) on copper ethernet, fiber is likely cheaper, and it's definitely more robust. I've never replaced a fiber for a nearby strike, but it's not uncommon to need to replace surge protectors after a storm.
If there's a clear shot, point to point wireless also works well, and may feel more accessible (fiber is not all that difficult, but it can feel daunting to get started with.)
There's really no advantage to using copper wires .vs. appropriately sized aluminum wires for the other two circuits. A thing you might want to consider would be skipping the DC circuit entirely by putting an inverter at the barn.