Can I use both, or do they interfere?
To my knowledge, they do not interfere with each other. They use completely different frequencies, it’d be like using 900mhz & 2.4Ghz cordless phones in the same house. Or “normal” wifi & 5G.
Both have their strengths & weaknesses, and I can see situations where it might make sense to use both and connect them through software like Home Assistant.
You’ll have to have the right hub or multiple chips connected to use them both, though, which would add a bit of extra cost to your overall system. But if you’ve already invested in the devices, that might not be an issue. 
You can definitely use both. Just a note that there is currently a PR that should be merged in soon that will bring native ZHA (Zigbee Home Automation) capabilities to HASS.
I’m using a Z-Wave/Zigbee combo USB stick on my Raspberry Pi with good success. You can also use something like a SmartThings bridge, since ST supports both Zigbee and Z-Wave as well.
I was in a position where I already had some Zigbee lights that I didn’t want to get rid of, but if you can stick with just Z-Wave, it’d probably make your life a little easier.
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Thanks for your fast response guys! I will definatly expand my home-assistant installation with some awesome Z-Wave devices.