There are several considerations and practices concerning interfaces
Some developers say that interfaces can be used as a replacement of multiple inheritance mechanisms, which cause complexity and ambiguity. But each feature must be implemented each time it is declared: this is not an inheritance, this is a wrapper to the description of a part of a group of classes, like IDisposable. It is the same as a multiple inheritance with one implemented class and some abstract classes: it is a particular case which allows only one way hierarchy with interfaces as abstract connectors that describes services.
Some developers say that interfaces can be used to separate the access to an object of this instance. Historically, interfaces are a COM & DCOM heritage: they are used to manipulate components services, whatever objects are, where they are, and how they are implemented. Interfaces are not a replacement to multiple inheritance, they are something else.
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A plea for full multiple inheritance support in .NET
A Typed Intermediate Language for Compiling Multiple Inheritance