You are required to have a valid travel document upon entering Switzerland if you are a "third country national."
According to this link: the travel document must:
"remain valid for at least three months after the intended date of departure from Switzerland; and
has been issued within the previous 10 years."
In practice, there are few border checks in the Schengen area if you are travelling by car or train, but oftentimes, by plane they check.
It's not really exactly the same case, but just as an example innthe Schengen area: a friend of mine who lives in Geneva (and almost quite lterally next to the border with the town of Ferney-Voltaire in France) wanted to go to Ferney-Voltaire and walked to the border. However, French police were doing checks at that time. He didn't have his passport with him, just his Swiss residence card. He was denied entry because of this (and was given a piece of paper stating that he was denied entry and explaining why).
I've dug a bit deeper into this, and this is what another page (section 3 of the FAQ of the Swiss State Secretariat for Migration). Three answers are relevant to your question:
One question asks:
Are citizens of a non-EU or EEA member state who are subject to visa requirements admitted into Switzerland if they travel on an expired passport or if their passport has been annulled but still contains a valid visa?
Entry into and stay in Switzerland will be approved if upon request the following documents can be presented:
- A passport expired or annulled containing a valid visa
- an officially recognized and valid passport (without visa).
Refusal of entry for other reasons remains explicitly reserved.
And the other question on:
Validity of travel documents of third-country nationals
Regardless of their visa obligation status, third-country nationals wishing to enter Switzerland for a short-term stay not exceeding 90 days per 180-day period must be in possession of a travel document that:
- will remain valid for at least three months after the intended date of departure from Switzerland; and
- has been issued within the previous 10 years.
Further down, it states:
The aforementioned provisions on the validity of travel documents do not apply to travel documents of third-country nationals who hold a valid residence permit issued by a Schengen country (Annex 22 Schengen Handbook) or who have been issued valid category D visa for a longer-term stay in a Schengen country. In such cases, the travel document must be valid at the time of entry and remain valid for the entire duration of the planned stay in Switzerland or other Schengen country.
In addition, the EU's website on travel documents for non-EU nationals says:
Passport and visa requirements
If you are a non-EU national wishing to visit or travel within the EU, you will need a passport:
- valid for at least 3 months after the date you intend to leave the EU country you are visiting,
- which was issued within the previous 10 years
As I mentioned above and based on these links, in theory, you have to have a valid travel document on you (and not just the resident permit), even when travelling within the Schengen.
However, in practice, there are very few checks within the Schengen area. If you do become subject to a random ID check inside Switzerland (which, I hear, is rather rare), your resident permit might suffice - based on what's said in the other posts - but they could make life really hard for you if they wanted to.
To be safe, I would not recommend travelling without a passport (as a third-country national), even if it's within the Schengen area and especially if you are flying.
(p.s. Another post with a similar question can be found here)