An interface can have a static constructor, which can be used to initialize static data members. A static constructor will be called at most once, and will be called before the first time a static interface member is accessed.
For more information on static constructors, see How to: Define Static Constructors in a Class or Struct.
Example
// mcppv2_interface_class2.cpp
// compile with: /clr
using namespace System;
interface struct MyInterface {
   static int i;
   static void Test() {
      Console::WriteLine(i);
   }
   static MyInterface() { 
      Console::WriteLine("in MyInterface static constructor");
      i = 99;
   }
};
ref class MyClass : public MyInterface {};
int main() {
   MyInterface::Test();
   MyClass::MyInterface::Test();
   MyInterface ^ mi = gcnew MyClass;
   mi->Test();
}
in MyInterface static constructor
99
99
99