Interfaces do not have access modifiers in their methods, leaving them open to whichever access modifier is appropriate. This has a purpose: it allows other types to infer what methods and properties are available for an object following an interface. Giving them protected/internal accessors defeats the purpose of an interface.
If you are adamant that you need to provide an access modifier for a method, either leave it out of the interface, or as you said, use an abstract class.
