Yes, like Serg said, you can mock this by providing an interface for the real service to implement. This interface would have the public methods you are calling, such as:
public interface IMyServiceInterface
{
IMembershipUser GetUser();
// other methods you want to use...
}
In your unit tests, you would say:
var mockService = new Mock<IServiceInterface>();
mockService.Setup(mock => mock.GetUser()).
Returns(new MembershipUserImplementation("MyTestUser", otherCtorParams));
In my example I would create a wrapper for MembershipUser as well as it seems like it also needs to be behind an abstraction.