This is known as surcharging. The rules differ by country, the same goes for interchange. To give you an example: my country it was forbidden to forbid the merchants to do surcharging (no really). Essentially the merchants where allowed to do surcharging. Then interchange was regulated down and the ban on forbidding surcharging was lifted. In theory the acquirers or payment schemes could forbid the merchants to do surcharging. AFAIK none of them did.

What you can do as a card holder is file a charge back over the surcharge amount. These get accepted.