Yes you can.

If you travel via Switzerland yes, If you travel via Italy no.

There is a direct Bus from Lugano to Tirano included but a reservation needed.

We have a interrail one countrypass so we do not want to take the bus and no seat reservation bernini train. We want to take the regional train Lugano and final station Chur. Is it possible?

There are no direct trains between Lugano and Chur. Or do you mean Tirano ?

To do the journey on a convenient route (one-country pass valid), it is the advertised route that you've seen I'm sure :

- Lugano - Tirano bus (pass valid, reservation needed). Very nice route along Lake Como. 10:00 - 13:00

- Tirano - Chur regional trains or direct Bernina Express (please use the reservation-free coaches, they're much better) 14:24 - 18:22 (or any other train with changes). There is a 13:41 train to St. Moritz (arrival 16:11).

Otherwise it is a really long detour (and not what you want !) :

- Lugano - Zurich - Chur

- Lugano - Bellinzona - Göschenen - Andermatt - Disentis/Mustér - Chur

- Lugano - Arth-Goldau - Pfäffikon SZ - Chur

All other options would include a bus journey that you'd need to pay (San Bernardino route) or trains in Italy (pass not valid)

Let us know.

Thank you for reply. I like to travel from tirano to chur via st. Moritz by regional train not Bernini train but it is the same route.

Yes it's possible. Simply take any hourly regional train between Tirano and St. Moritz (if you see a AW symbol in SBB app, there will be some open-air coaches).

St. Moritz - Chur : hourly IR train

It's easy, don't worry. You can look at SBB app (or sbb.ch) to see the connections.

I recommend a stop in Alp Grüm along the way if you can. Then take the next train about an hour later :)

The Bernina Railway is my favourite of the country, you'll love it !

You say via Italy nu regional train it is not possible by interrail 1 country switzerland for free but with SBB it should be according to other replies. 

It is a pity I have to ask in this forum other interrailusers and the interrailservicedesk itself doensn't answer my question. Now i have received different explainations..

Here's a map with the validity of an Interrail for Switzerland:

https://www.sbb.ch/content/dam/infrastruktur/trafimage/karten/karte-geltungsbereich-InterRail-EuRail.pdf

As you can see, a bus Lugano-Tirano is included but the train in that part of Italy is not.

I'd be surprised if SBB say anything else.