Names and prices can be confusing on Interrail website. Best book through the railway company : likely Nightjet per your post. Go to nightjet.com and add Interrail as a discount.

Prices on Interrail should be (incl. 2€ fee which you can avoid) : 5€ for a 1st or 2nd class seat and 41€ for a bunk/couchette in a 4-6 person compartment. Sleepers are more expensive but then you save a night accommodation.

More info : https://www.seat61.com/interrail-and-eurail-reservations.htm

Feel free to ask further questions, mentioning if possible route and travel date. :)

Okay then, from what I have read, with a first or second class reservation I can get a bunk bed no matter what, without having to pay €41, right?

I have read it here : https://www.seat61.com/interrail-and-eurail-reservations.htm#Italy 

This is what it says on that page.

Option 3, using the Eurail/Interrail reservations service

The Eurail/Interrail reservations service can also make reservations for sleepers & couchettes on InterCity Notte trains, but there's a problem.  If you have a 2nd class pass it only offers couchettes, even though you're entitled to book single or double sleepers with a 2nd class pass.  So if you have a 2nd class pass and want to book a single or double sleeper, use option 3 below.

What route do you want to travel?

For Italian night trains it's best to use ItaliaRail as suggested by Seat61 : https://partners.italiarail.com/default?force_pass=true&aff=S61U

But first check how much is an advance ticket on your date. They're often not more expensive than the reservation (especially if you save a pass day) and you can get a private cabin.