I see this is a .Net question; however, the thinking may be coming from a Java background. It reminds me of Item 22 from Effective Java: Use Interfaces only to define types.
This recommendation does not proscribe all properties in interfaces. It specifically addresses interfaces containing only properties.
When a class implements an interface, the interface serves as a type that can be used to refer to instances of the class. That a class implements an interface should therefore say something about what a client can do with instances of the class. It is inappropriate to define an interface for any other purpose.
One kind of interface that fails this test is the so-called constant interface. Such an interface contains no methods; it consists solely of static final fields...
The constant interface pattern is a poor use of interfaces. That a class uses some constants internally is an implementation detail. Implementing a constant interface causes this implementation detail to leak into the class's exported API... it represents a commitment: if in a future release the class is modified so that it no longer needs to use the constants, it still must implement the interface to ensure binary compatibility. If a nonfinal class implements a constant interface, all of its subclasses will have their namespaces polluted by the constants in the interface.
Of course, Java itself (and probably C#) contain examples of these constant interfaces. The book addresses that as well.
There are several constant interfaces in the Java platform libraries... These interfaces should be regarded as anomalies and should not be emulated.
I agree with previous answers that I have never seen a recommendation to avoid interfaces containing both properties and methods.